LCM for 8, 10 and 12

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

What's the Least Common Multiple (LCM) of 8, 10 and 12?

Answer

LCM of 8, 10 and 12 is
120

(One hundred twenty)

120 is the smallest positive integer that 8, 10 and 12 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 10 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 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

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

Prime factor81012Highest power
22322223
3——33
5—5—5

LCM = 23 × 3 × 5 = 120

Checking the LCM of 8, 10 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(8, 10) = (8 × 10) ÷ 2 = 80 ÷ 2 = 40

LCM(40, 12) = (40 × 12) ÷ 4 = 480 ÷ 4 = 120

LCM(8, 10, 12) = 120

The pairs may be taken in any order — 10 and 12 first, then 8 — and the answer is the same 120. That is exactly why the two routes on this page agree.

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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 8, 10 and 12? (The answer is: 120). Enter the first number (e.g. '8'), the second (e.g. '10') 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
181040
281040
3810120
481040
581040
6810120
7810280
881040
8910360
8101040
81011440
81012120
81013520
81014280
81015120
8101680
81017680
81018360
81019760
8102040
81021840
81022440
81023920
81024120
81025200
81026520
810271,080
81028280
810291,160
81030120

FAQ

What's the Least Common Multiple (LCM) of 8, 10 and 12?

LCM of 8, 10 and 12 is 120

How to find the LCM of 8, 10 and 12 by prime factorization?

Take every prime that appears in 8, 10 and 12 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 8, 10 and 12 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 10 is 40, and the LCM of 40 and 12 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 8, 10 and 12?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 8, 120 ÷ 10 and 120 ÷ 12 all come out whole. Any other common multiple of 8, 10 and 12 is a multiple of 120.

See Also