Question 990447: Hay's Linens sells hand towels in sets of 10 and bath towels in sets of 6. If the store sold the same number of each [LCM] type of towel that the store must have sold?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Selling hand towels in sets of  , the number of hand towels sold must be a multiple of .
Selling bath towels in sets of  , the number of hand towels sold must be a multiple of .
If the store sold the same number of each type of towel,
that same number of each type of towel sold must be a multiple of , and .
The smallest possible number of each type of towel sold is the least common multiple (LCM) of , and .
That number is  .
Of course, the store may have sold
 of each type of towel, or
 , or  , or ...
HOW TO FIND THE LCM:
1) We could list the multiples of one of the numbers (preferably the largest).
The multiples of are:
,  ,  ,  , ...
Then we would check then one by one, from smallest to largest,
to see if we can find a multiple of the other number(s).
In this case, , and are not multiples of ,
but is, so is the LCM of , and .
2) Sometimes the method above does not give you the answer fast enough.
A more general method involves finding the prime factorizations.
The prime factorizations of , and are
 and  .
The prime factorization of the LCM includes all prime factors found in the numbers, with the greatest exponents (if any).
In this case,
 ,
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