LCM for 6, 8 and 12

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

What's the Least Common Multiple (LCM) of 6, 8 and 12?

Answer

LCM of 6, 8 and 12 is
24

(Twenty-four)

24 is the smallest positive integer that 6, 8 and 12 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 6, 8 and 12 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 6: 2 × 3 (exponent form: 2 × 3)

All Prime Factors of 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

Prime factor6812Highest power
22232223
33—33

LCM = 23 × 3 = 24

Checking the LCM of 6, 8 and 12 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(6, 8) = (6 × 8) ÷ 2 = 48 ÷ 2 = 24

LCM(24, 12) = (24 × 12) ÷ 12 = 288 ÷ 12 = 24

LCM(6, 8, 12) = 24

The pairs may be taken in any order — 8 and 12 first, then 6 — and the answer is the same 24. That is exactly why the two routes on this page agree.

Related Calculations

See Also

About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 6, 8 and 12? (The answer is: 24). Enter the first number (e.g. '6'), the second (e.g. '8') and the third (e.g. '12'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
16824
26824
36824
46824
568120
66824
678168
68824
68972
6810120
6811264
681224
6813312
6814168
6815120
681648
6817408
681872
6819456
6820120
6821168
6822264
6823552
682424
6825600
6826312
6827216
6828168
6829696
6830120

FAQ

What's the Least Common Multiple (LCM) of 6, 8 and 12?

LCM of 6, 8 and 12 is 24

How to find the LCM of 6, 8 and 12 by prime factorization?

Take every prime that appears in 6, 8 and 12 to the highest power it reaches in any one of them and multiply: 2³ × 3 = 24.

Can you get the LCM of 6, 8 and 12 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 6 and 8 is 24, and the LCM of 24 and 12 is 24 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 24 divisible by 6, 8 and 12?

Yes, and by definition it is the smallest positive integer that is: 24 ÷ 6, 24 ÷ 8 and 24 ÷ 12 all come out whole. Any other common multiple of 6, 8 and 12 is a multiple of 24.

See Also