Topic 2

Factors, multiples, GCF & LCM

A factor divides a number with no remainder. A multiple is what you get by multiplying that number by 1, 2, 3, and so on. GCF means greatest common factor; LCM means least common multiple.

Class slides 19–28

How to answer questions

For factors, make pairs that multiply to the number. Compare the two factor lists to find the GCF.
For multiples, skip-count by each number. Find the first shared result to get the LCM.
In a word problem, use GCF to make the largest equal groups; use LCM to find when different cycles match up.

Worked example

Use 12 and 18:

Factors of 12: 1, 2, 3, 4, 6, 12Factors of 18: 1, 2, 3, 6, 9, 18

The largest shared factor is 6, so GCF = 6. Their multiples first meet at 36, so LCM = 36.

How to prepare

Make factor-pair lists and skip-counting lists for small numbers. Ask yourself: “Am I dividing into groups, or looking for a first shared total?”

Watch out: A factor of 12 is usually smaller than or equal to 12; its multiples keep going forever.

Try it:

Hot dogs come in packs of 6 and buns in packs of 8. What is the smallest equal number of each you can buy?

I can do this

Show answer

Find the LCM of 6 and 8: 24. Buy 4 packs of hot dogs and 3 packs of buns.

More practice · 3 questions

Try all three before you open the solutions.

Warm-up

List every positive factor of 24.

Show solution

Make factor pairs: 1 × 24, 2 × 12, 3 × 8, and 4 × 6. The factors are 1, 2, 3, 4, 6, 8, 12, 24.

Practice

Find the GCF of 18 and 30.

Show solution

Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. The greatest shared factor is 6.

Challenge

Two lights flash every 9 seconds and every 12 seconds. When will they next flash together?

Show solution

Find the LCM: multiples of 9 are 9, 18, 27, 36; multiples of 12 are 12, 24, 36. They next flash together after 36 seconds.