GCF and LCM · part 6 of 7
Why Do We Need This?
Reducing a fraction in one step, and the common denominator.
So why does anyone care?
Because these two are the tools for the two most annoying things you do with fractions.
The GCFreduces a fraction in one go
The GCF of 24 and 36 is 12, so write both of them that way:
2436 = 2 × 123 × 12
Same number top and bottom. That is 1212, and 1212 is 1.
= 23 × 1 = 23
You did not cancel anything. You found a 1 that was hiding, and took it out.
Divide by anything smaller than the GCF and another 1 is still in there.
The LCMis the common denominator
To add 124 + 136 the two pieces have to be the same size, so you need a number that both 24 and 36 divide into. That is exactly the least common multiple: 72.
72 ÷ 24 = 3, so 124 = 372
72 ÷ 36 = 2, so 136 = 272
372 + 272 = 572
Using the least one keeps the numbers small. 24 x 36 = 864 works too, but then you are reducing afterwards.
Same two numbers, one picture, both jobs. That is why the picture is worth drawing.