   SEARCH HOME Math Central Quandaries & Queries  Question from parth, a student: name 3 consecutive numbers,each less then a 100,the smallest # is divisible by 6 the next is divisible by 5 and the largest divisible by 4 Hi,

Since the smallest number is divisible by 6 it is one of

6, 12, 18, ...

Since the smallest number is divisible by 5 it is one of

5, 10, 15, ...

Continue the two lists until you find a pair so that the number in the first list is less than a number in the second list. Add 1 to the number in the third list so that you have three consecutive numbers with the smallest divisible by 6 and the next divisible by 5. Is the third divisible by 4? It's not so you are not finished.

You can continue the two lists above but there is an observation that makes the problem easier than that. The first list goes up in steps of size 6 and the second list goes up in steps of size 5 so the next time they are 1 number apart results from a step of size $6 \times 5 = 30.$ Hence add thirty to each of the numbers in the triple in the previous paragraph. You again have three consecutive numbers with the smallest divisible by 6 and the next divisible by 5. Is the third divisible by 4?

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.