Given any two numbers, which is greater, the lcm of the numbers or the gcf of the numbers? why?

LCM stands for Least Common Multiple while GCF stands for Greatest Common Factor.

Given any two numbers, LCM of the numbers is greater than the GCF of the numbers.

Because LCM multiplies all the multiples of both numbers while GCF multiples only the factors found in both numbers.

For example: 3 and 8

3 =              3
8 = 2    2    2

Even though 3 and 8 has no common factor, their GCF is equal to 1. Since 1 divides into everything.

LCM of both numbers would be  2 x 2 x 2 x 3 = 24.

Thus in any two given numbers, LCM is greater than GCF.