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