Question

If the Greatest Common Factor of L and M is 6, write the expression for the Least Common Multiple of these numbers.

Answer 1

Answer:  

$\frac{(L x M)}{6}$

Step-by-step explanation:  

The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.

The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.

We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.

As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.  

We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.

$\frac{(L x M)}{6}$