Maths question on Factors and Primes

Question

A rambler club buys hats in packs of 12 and scarves in packs of 18. The club buys exactly the same number of hats and scarves.

 

What is the smallest number of packs of hats and the smallest number of packs of scarves the club buys?

 

Answer 1

The prime factors:

    of 12:        2*2*3

    of 18:        2*3*3

 

The LCM (Least Common Multiple; because "The club buys exactly the same number of hats and scarves") of 12 and 18 is 2*2*3*3=36 (it contains all of the factors).  So, if the club buys 36 hats (that is, 3 packs) and 36 scarves (that is, 2 packs), they will have the smallest same number of hats as scarves.