im thinking of two number thier GCF is 2 and thier LCM is 60.your numbers must be 10 and 12 is leillah right or wrong explain

Question

if u agree with leillah explain how you know these numbers and only these numbers work.

if you disagree find all posible pairs of numbers that mses might be thinking of.

Answer 1

Let a and b be the numbers, both numbers must be even if 2 is the GCF, so let a=2m and b=2n where m and n are integers. m and n have no other factors in common, so mn is their LCM and the LCM of a and b is 2mn=60 and mn=30, which has factors 1 and 30, 2 and 15, 3 and 10, 5 and 6.

So a and b can be 2 and 60, 4 and 30, 6 and 20, 10 and 12.

Leillah is wrong in thinking that a and b can only be 10 and 12.