# Question #585c4

##### 1 Answer

The only way that the GCF of two numbers could be their product is if both numbers are 1 (that way the product isn't bigger than either of the numbers). And the LCM of 1 and 1 is

#### Explanation:

Hmm... factors of a number cannot be bigger than the number itself. In mathematical terms,

#"number " >= " factor of that number"#

But, we see here that we have two positive integers

#ab# is a factor of both#a# and#b#

This means that

We can do a bit of algebra to determine what these two numbers must be:

#a >= ab " "" "and" "" "b >= ab#

Divide both sides of the first inequality by

#a/a >= (ab)/a " "" " and " "" " b/b >= (ab)/b#

#1 >= b " "" " and " "" " 1 >= a#

So both

The LCM of *final answer*.