SOLUTION: 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?

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 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?       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



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) About Me  (Show Source):
You can put this solution on YOUR website!
Selling hand towels in sets of 10 , the number of hand towels sold must be a multiple of 10 .
Selling bath towels in sets of 6 , the number of hand towels sold must be a multiple of 6 .
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 10 , and 6 .
The smallest possible number of each type of towel sold is the least common multiple (LCM) of 10 , and 6 .
That number is highlight%2830%29 .
Of course, the store may have sold
2%2A30=60 of each type of towel, or
3%2A30=90 , or 4%2A30=120 , or ...

HOW TO FIND THE LCM:
1) We could list the multiples of one of the numbers (preferably the largest).
The multiples of 10 are:
10 , 20 , 30 , 40 , ...
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, 10 , and 20 are not multiples of 6 ,
but 30 is, so 30 is the LCM of 10 , and 6 .
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 10 , and 6 are
10=2%2A5 and 6=2%2A3 .
The prime factorization of the LCM includes all prime factors found in the numbers, with the greatest exponents (if any).
In this case,
LCM%2810%2C6%29=2%2A3%2A5=30 ,