Here is a fast and simple way to find GCF and LCM without prime factorization. Start by getting three numbers and lining them up side by side.

10 14 20

Now find a common factor all three of them have. Divide all the numbers by 2.

10 14 20
5 7 10

After this step you notice that 5,7 and 10 are prime and no other numbers can go into them. Making 2 the GCF. We have now successfully found the GCF, but to find the LCM we will continue with the same numbers. We need to find a number that goes into a pair of remaining numbers. 5 goes into 5 and 10, so divide both by 5.

10 14 20
5 7 10
1 7 5

Take note that if the 5 doesn’t go into a number, it stays as is. So 7 will remain 7. Now check if there are any numbers that can fit into the remaining ones. Since 1,7 and 5 are prime they will stay like this. Now you take 2, 5 (the numbers you divided by) 1,7 and 5 (the remaining numbers). We ignore the 1.

LCM = 2x5x2x7
= 140
try again but with bigger numbers. Divide by a common multiple, 6.

156 138 204
26 23 34

Since 23 is not longer divisible, the GCF is 6. Use the same numbers to find the LCM. Find a number that fits into a pair of numbers. 2 fits into 26 and 24 so use that.
156 138 204
26 23 34
13 23 17

Now take the numbers you divided by (2,6) and the numbers leftover and multiply.

LCM= 6x2x13x23x17
= 60996

I definitely prefer the method we were taught in class compared to this one. Prime factorization is easier and takes less time to do. Prime factorization is the most common method for a reason, it’s the best. The picture is an example of prime factorizatio.