







Two people are clapping their hands 
20191206 

From Yukti: Two people are clapping their hands, but with different frequencies. Ramya claps her hands
17 times per 3 minutes, and Kumar claps his hands 31 times per 5 minutes. They start
clapping at the same time. How many times does each one clap before they clap together at
the same time again? Answered by Penny Nom. 





Packing chocolates in boxes 
20190722 

From CHESKA: 1.levy can pack the chocolate bars either with 35 bars in a box,with 42 in a box, or with 49 in a box. what is the least number of chocolate bars that he has?
2. the blue light of a Christmas light blinks every 2 second. the red light blinks every 3 second and the yellow light blinks every 5 second. how many times will the three lights blink at the same tims in one hour?
3.a wooden straightedge can exactly measure an 825 cm rope, a675 cm rope, and 375 cm rope. what is the least possible length of the straightedge? how many times will it measure each rope? Answered by Penny Nom. 





An airplane schedule 
20161014 

From Stephanie: Starting at 8:00a.m., a passenger plane leaves from an airport every 6 minutes and a cargo plane leaves every 7 minutes. When is the next time these kinds of planes will leave at the same time? Answered by Penny Nom. 





HCF and LCM 
20150905 

From Ally: the HCF of the two numbers is 3, and the LCM is 15.
what could the two numbers be? Answered by Penny Nom. 





HCF and LCM 
20130515 

From Kelly: If HCF and LCM of two numbers is 7 and 20 respectively, then the number/s is/are…. Answered by Penny Nom. 





Gray siding and stone chimneys 
20120422 

From lupita: Fifty houses are on the north side of a river. The 2nd house has gray siding, and every 5th house after that also has gray siding. The 11th house has a stone chimney; every 3rd house after that also has a stone chimney. How many of the 50 houses have stone chimneys but do not have gray siding? Answered by Penny Nom. 





Repeating a medication 
20111202 

From ivan: One person received the recommendation of a doctor taking the drug "Passaneura" every 10 hours. After a few days, noted that the time you should take the medication had not been repeated once. How many days since the first dose, will have to pass the time until recur Answered by Penny Nom. 





The LCM of 6,15 and x is 90 
20111030 

From Richie: Hi there,
There are 2 parts to the question.
#1. Factorise 90. This is easy, 90=2x3x3x5
#2
LCM of 6,15 and x is 90. What are possible values of x if x is odd?
From #1, since 90=6x15, how can this be used to work out possible values of x?
Thanks in advance,
Richie Answered by Penny Nom. 





x/200+x/400+x/600+x/800 
20101008 

From Ashishthombre: step by step LCM of x/200+x/400+x/600+x/800 Answered by Penny Nom. 





Two bus routes 
20100203 

From kiyah: from 4:30 pm to 6:30 pm the route 1 bus stops every 12 min at the gym's bus stop. the route 2 bus stops there every 15 min. if both buses are now at the stop and schedule is kept, how long will it be before both buses will be at the stop again? Answered by Penny Nom. 





The product of two integers their LCM and their HCF 
20090215 

From Anonymous: Two numbers have LCM = 60. If their product is 180, what is their HCF? Answered by Harley Weston. 





Lita and Rose start jogging on a 110 m circular track 
20090113 

From Narcisa: Lita and Rose start jogging on a 110 m circular track. They begin at the same point, but jog in opposite directions, lita at 8/3 meters per second and rose at 7/3 m per second. Find the number of times they they will pass each other during the first 15 minutes of jogging? Answered by Robert Dawson. 





LCM and GCD 
20080522 

From kasirao: Please help me in knowing the proof for the equality,
"The product of two natural numbers is equal to their LCM and GCD" Answered by Penny Nom. 





Find two numbers with HCF of 3 and LCM of 180 
20080207 

From matthew: Hi, please help me with this, Find two numbers with HCF of 3 and LCM of 180 Answered by Stephen La Rocque and Penny Nom. 





GCF and LCD 
20080117 

From Peter: I need to know the differences between GCF and LCD. Answered by Penny Nom. 





LCM over 100 
20071209 

From Aris: A teacher has more than 100 sweets. She thinks that if she give 6, 8 or 9
sweets to her students she will have no remaining in the case. What is the
smallest number of sweets in the bag? Answered by Stephen La Rocque. 





The realtionship between lcm and gcd 
20071027 

From Brenda: why does multiplying lcm of (n,s) by gcd (n,s) give n times s. when (n,s) are any two numbers? Answered by Penny Nom. 





13 year and 17 year locusts 
20071012 

From stefan: how many years pass between the years when both 13 year and 17 year locusts are out at the same time? Answered by Penny Nom. 





Least Common Multiples 
20070920 

From Aiyanna: What is The Lcm Of 3,7,and 8 Because my Teacher gave me That and he didnt even know the answer....
I Worked and worked but I Couldnt Find It..... Answered by Penny Nom and Victoria West. 





The lcm of polynomials 
20070531 

From devin: x^38 , x^34, x^2+4x+4 Answered by Penny Nom. 





Least common multiple 
20061108 

From Melenie: I have a daughter in 5th grade she can't seem to grasp the concept of finding LCM's does anyone have a quick easy way for her to learn????? Answered by Stephen La Rocque. 





LCM and HCF 
20061028 

From Henry: Is there a unique solution to the question: If the LCM and HCF of two numbers are 180 and 15 respectively, what are the two numbers? I got 45 and 60. I got a feeling there are others. Answered by Stephen La Rocque. 





Least common multiple 
20060925 

From A student: What is the LCM of 10,45 and 38? Answered by Stephen La Rocque. 





HCF and LCM 
20060805 

From Bharath: The HCF and LCM of polynomials p(x) and q(x) are h and l respectively and p(x) + q(x) = h + l, show that
[p(x)]^{2} + [q(x)]^{2} = h^{2} + l^{2} Answered by Stephen La Rocque. 





The Least Common Multiple of two primes 
20060221 

From Kristine: Is the Least Common Multiple to two prime numbers always their product? Why or Why not? Answered by Stephen La Rocque. 





GCF, LCM, primes and the ladder method 
20060107 

From Linda: How would I teach both finding the GCF and LCM with prime factors...I recall the ladder method vaguely.??? Answered by Penny Nom. 





LCM 
20051212 

From Alex: what is the LCM of 210 and 54 and the LCM of 42 and 126 Answered by Penny Nom. 





Least common multiple 
20051022 

From Dayna: I'm stumped! I can't seem to come up with a least common multiple of 22 and 25. Is there one? Answered by Penny Nom. 





The lcm of 5, 3, 4, 7 and 2 
20041105 

From Christine: what is the lcm of 5,3,4,7,2 Answered by Penny Nom. 





The lcm of 1 and 1 
20041103 

From Nayiyan: I would like to know what is the LCM of (1) and (+1) is. Answered by Penny Nom. 





GCD and LCM 
20041031 

From Cartalina: how do you calculate the "positive difference between the GCF and LCM of two numbers"? Answered by Penny Nom. 





The Parliament of the land of Achronia 
20040529 

From Christine: The Parliament of the land of Achronia consists of two houses. The parliament was elected in 2003 for a period of six years beginning on Thursday, the 1st of January 2004, when the two houses had their first sessions. According to the rules, the meetings of the first house must occur every twelve days for the duration of the term, and the meetings of the second house must occur every eighteen days. For example, the second meetings of the first and the second houses were held on the 13th and 19th of January respectively. A new law can be passed on any day when both houses meet, except on a Thursday. On how many days can the parliament members pass new laws during this six year term? Answered by Penny Nom. 





The HCF and LCM of polynomials 
20030520 

From Charanpal:
Question: Find the HCF and LCM of the polynomials given below. Verify that he productof these HCF and LCM differs from the product of the polynomials, if at all, by a factor of 1  1x^{2} and x^{3} 1
 1  x^{2} and x^{4}  1
Answered by Penny Nom. 





Multiples of all four of the numbers 2, 3, 4, and 5 
20030211 

From Stephanie: How many of the first 1000 positive integers are multiples of all four of the numbers 2, 3, 4, and 5? Answered by Penny Nom. 





The least common denominator 
20030121 

From Brittan: Hi there I need help! My name is Brittany and i am in the 6th grade. I need help finding the least common denominator(LCD), and the book says Find the LCM of the denominators and i've done that and then it says write equivalent fractions,using the LCM as the least commonn denominator.The directions say Use the LCD to write each pair as like fractions. and the problem is 1/8 and 5/40. Could u explain how in the word u do this? Thanks a lot Brittany Answered by Penny Nom. 





Manufactures golf balls 
20011106 

From Kevin: A company manufactures golf balls. Golf balls are each numbered consecutively 0 to 4, and then the numbering starts over with zero again. Every 12th golf ball is yellow. Every 8th golf ball is tested for defects. The company produces 120,000 golf balls in an eighthour shift. A. How many yellow golf balls are tested for defects during the day? Explain your reasoning. B. How many of these yellow balls that are tested are imprinted with the numeral 2? Explain your reasoning. Answered by Penny Nom. 





Locusts 
20011008 

From A parent: JOHN CONJECTURED THAT BOTH 13YR.&17YR. LOCUSTS CAME OUT THE SAME YEAR. ASSUME IT IS CORRECT. HOW MANY YEARS PASS BETWEEN THE YRS. WHEN BOTH 13 YR. & 17YR. LOCUSTS ARE OUT AT THE SAME TIME? EXPLAIN. NEXT, SUPPOSE THERE WERE 12YR.,14 YR.,& 16YR. LO CUSTS,& THEY ALL COME OUT THIS YR. HOW MANY YRS. WILL IT BE BEFORE THEY ALL COME OUT TOGETHER AGAIN? Answered by Leeanne Boehm. 





GCD and LCM 
20010924 

From David: Find the GCD adn LCM of the following numbers. Assume p 2 to the power p, 3 to power q, 5 to power r and 2 to power q, 3 to power r, 7 to power p Answered by Penny Nom. 





A remainder of 1 
20010220 

From A student: what is the smallest positive integer which has a remainder of one when divided by 2,3,4,5 and 6 Answered by Penny Nom. 





A four digit number 
20010217 

From Dean: Need to find a 4 digit number that can be divided by 2, 3, 4, 5, 6, 7, 8, 9, and will always have a remainder of 1 in the answer. Answered by Penny Nom. 





Two number theory questions 
20010130 

From Richie: i have two questions and they are:  the product of three consecutive prime numbers is 7429. Find the product of the smallest and largest of these three integers.
 the least common multiple of two relatively prime positive integers, a and b, is 144. if a (a>or=2) is as small as possible, compute the value of b.
Answered by Penny Nom. 





Factoring, primes, GCF and LCM 
20000227 

From Ruth Kroek: My son is in grade seven, he has to do a Factoring Booklet the areas covered are:  Prime #'s
 Composite #'s
 Rainbow Factoring
 Finding Multiples (consecutive multiples)
 Finding GCF of 23 numbers uning Rainbow factoring
 Finding LCM of 2 numbers using consecutive multiples
 prime factor trees
 prime factor ladders
 finding GCF of 2 numbers using Prime number Method
Although his text 'Math Power' gives some information, we are at a loss .. Answered by Penny Nom. 





Least Common Multiple 
20000216 

From Kathy Heath: The way I understand it is for 2,3,9 the least common multiple is 18. Am I right? If so, I guess the least common multiple for 3,4,7 is 105. Please let me know if I'm right so I can tell my daughter. Answered by Denis Hanson. 





Jose and Arthur 
19990926 

From Joel Hammer: Jose can run around the track in 40 seconds. Arthur runs with Jose but in the opposite direction. They meet every 15 second. How long will it take Arthur to make one trip around the track? Answered by Denis Hanson. 





Where three sequences meet. 
19990306 

From Ali: My name is Ali and I am in the 5th grade. I have a math question: What is the least positive integer meeting each of the following conditions:  Dividing by 7 gives a remainder of 4
 Dividing by 8 gives a remainder of 5
 Dividing by 9 gives a remainder of 6
Help! Answered by Denis Hanson. 





Greatest Common Factor. 
19980109 

From Percy Stribling: how do you figure out what the greater common factor is? Answered by Penny Nom. 





Two Questions 
19970828 

From Faye Tan: I am a trainee teacher. I would appreciate it very much if you could help me solve the following two problems which I think are meant for students at middle grade. 1. If a hen and a half lays an egg and a half in a day and a half, how many hens are needed to lay a dozen eggs in one day? 2. There are fewer than 200 passengers on a train. If they get off in pairs, one passenger will be without a partner. If they get off in groups of 3 or 4, there will still be one passenger left by himself. However, if they get off in groups of 5, no one will be left by themselves. How many passengers are there on the train? Answered by Penny Nom. 





How many digits are there in 2^2520? 
19961007 

From Rita Leung: A)The number 64 is a sq., a cube, and a sixth power because 64=8*8, 4*4*4, 2*2*2*2*2*2. Find the smallest integer greater than 1 that is a sq., a cube, a 4th, 5th, 6th, 7th, 8th, 9th and 10th power. I have found that the answer is 2 to the power 2520th. B) How many digits are in the correct answer to part A? The answer is uncertain. It is either 758 or 759. Can you give me any ideas? Answered by Penny Nom. 

