How to find the least common multiple (LCM)

The least common multiple (LCM) of two numbers is the smallest number both divide into. For 4 and 6 it is 12. Find it by listing multiples or by prime factorization. This page shows both methods, has an LCM finder, and explains where the LCM is used: common denominators and things that repeat on a schedule.

Method 1: list the multiples

Multiples of 4: 4, 8, 12, 16, 20, 24…
Multiples of 6: 6, 12, 18, 24…
The first one they share is 12.

Tip: list multiples of the bigger number and check each one against the smaller.

Method 2: prime factorization

4 = 2 × 2 and 6 = 2 × 3. Take each prime the most times it appears in either: two 2s and one 3. 2 × 2 × 3 = 12.

LCM finder

The first shared multiple is highlighted.

Where the LCM is used

Common denominators: to add 1/4 + 1/6, use LCM(4, 6) = 12. See adding fractions.
Things that repeat: one bus every 12 minutes and another every 18 minutes leave together again after LCM(12, 18) = 36 minutes.
Buying in packs: hot dogs in 10s and buns in 8s: buy 40 of each so none are left.

Common mistakes

LCM of 4 and 6 = 24Multiplied the numbers.Fix: 24 is a common multiple but 12 is the least.

LCM of 4 and 6 = 2Found a common factor.Fix: the LCM is at least as big as the bigger number.

Stopped listing too earlyNo common multiple found in the first three.Fix: keep going; it is always there by a × b.

Used GCF for “when together again”Mixed up the two.Fix: repeating schedules and common denominators → LCM.

How to teach it at home

Bus timetables

Two buses every 10 and 15 minutes: when do they leave together? (30)

Hot dogs and buns

Packs of 10 and 8: how many of each to match? (40)

Clap patterns

One person claps every 3 beats, another every 4: when do they clap together?

By grade

Grade 4: multiples.
Grade 5: common denominators when adding fractions.
Grade 6 (6.NS.B.4): LCM of two numbers up to 12.
See also greatest common factor.

Worksheets and practice

Least common multiple worksheet: printable PDF with an answer key. · Make a fresh test

GCF and LCM mixed (PDF) · All factors and multiples

Last reviewed October 3, 2026

Questions parents ask

What is the LCM?

The least common multiple: the smallest number that two or more numbers all divide into. LCM(4, 6) = 12.

How do you find the LCM?

List multiples of each number until you find the first one they share, or multiply each prime the most times it appears in either number.

Is the LCM always the two numbers multiplied?

Only when they have no common factor except 1, like 4 and 9 (LCM 36). Otherwise it is smaller: LCM(4, 6) = 12, not 24.

What is the LCM used for?

Finding common denominators, and working out when repeating events happen together.

What is the relationship between GCF and LCM?

GCF × LCM = the product of the two numbers. For 4 and 6: 2 × 12 = 24 = 4 × 6.