Question

Find the smallest value of n such that the LCM of n and 15 is 45.

Answer 1

i hope this helps answer your question. i believe the answer is 5.

Answer 2

Solution:

we have been asked to find

The smallest value of n such that the LCM of n and 15 is 45.

The prime factors of 15 are

$15=3*5$

So in LCM of n and 15 , we must include both the prime factors and the LCM is 45.

Since 3 is one time in the prime factor of 15. But to make 45 we need one more 3 and its possible if we take the value of n as below"

n=9

$9=3*3=3^2$

Hence the LCM will be

$3^2*5=45$

Hence the smallest possible value of n is 9.