Find the Least Common Multiple

Students find the least common multiple (LCM) of two whole numbers up to 12 by listing multiples and using prime factorization. They apply the LCM to solve real-world problems involving repeating events and to add and subtract fractions with unlike denominators.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Grade 6 · Greatest Common Factor and Least Common Multiple · question 1 of 3

0 of 20

20 rungs. A star at the top.

2 and 5 share many multiples. Which of these is NOT one of them?

How it is taught

0:00 of 3:34

A multiple is a number you land on when you skip-count.

The least common multiple is the smallest number in both lists.

Read it: The least common multiple

Count by 4: 4, 8, 12, 16. Count by 6: 6, 12, 18. The first number on both counts is 12, so the least common multiple of 4 and 6 is 12.

Count by each number.
Find the first number on both counts.
That number is the LCM.

A common multiple is a number both counts land on.

The product, 4 × 6 = 24, is a common multiple, but the counts meet first at 12.

12 = 4 × 3 and 12 = 6 × 2.

Count by both numbers; the first number on both counts is the LCM.

Multiplying them: 4 × 6 = 24.

24 is a common multiple, but the counts meet first at 12.

The LCM of 10 and 12 is ___ — 60. Count by 12 until a number is also a multiple of 10: 60 = 10 × 6.

LCM(4, 6)

Hot dogs come in packs of four. Buns come in packs of six. What's the smallest number where we'd have the same of each?

We need the Least Common Multiple of four and six — the smallest number that's a multiple of both.

Let's list multiples of four: four, eight, twelve, sixteen, twenty, twenty-four.

Now multiples of six: six, twelve, eighteen, twenty-four.

Look! Twelve appears in both lists.

Twenty-four is in both lists too. So twelve and twenty-four are common multiples.

Grade 6 · The smallest number that is a multiple of both 4 and 6

We want the least — the smallest. Twelve is smaller than twenty-four, so twelve is our LCM.

The LCM of four and six is twelve. We'd need twelve hot dogs and twelve buns to match. Nice work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free