Plot the nonzero multiples of the numerator and the denominator on separate number lines

I don't see any fractions.

Let's me make up an example:

8/12

Non-zero multiples of 8:

1 x 8 = 8

2 x 8 = 16

3 x 8 = 24

4 x 8 = 32

5 x 8 = 40

etc.

Non-zero multiples of 12:

1 x 12 = 12

2 x 12 = 24

3 x 12 = 36

4 x 12 = 48

etc.

Plot the multiples on two parallel number lines. You'll see that 24 is the first place where they share a multiple. That's the "least common multiple" of those two numbers.

LCM (8,12) = 24