my name is richie
my question type is secondary
my teacher is asking the questions

i have two questions and they are:

1. the product of three consecutive prime numbers is 7429. Find the product of the smallest and largest of these three integers.
   
   
2. 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.

Please show me how you solved these problems

thank you!

For problem 1 notice that 20³ = 8000 so the middle prime is probably slightly smaller than 20.

For problem 2 the lcm of a and b is 144 = 2⁴ x 3². Thus a = 2^s x 3^t and b = 2^u x 3^v for some integers s, t, u and v. Since a>or=2, either s is not zero or t is not zero. What does the fact that a and b are relatively prime tell you about s, t, u and v?