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

Let's look at some examples of LCM and GCF of numbers:

3,5
LCM: 15
GCF: 1

2,4
LCM: 4
GCF: 2

Thus, the LCM is always greater.
Why? Because the whatever common factor, can always multiply something and get the LCM. So no matter what two numbers they are, their GCF is always one of the factors of their LCM. 

Look at the two examples above: 
3,5
1(GCF) is a factor of 15(LCM)

2,4
2(GCF) is a factor of 4(LCM)

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