LCM for 10, 11 and 12

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

What's the Least Common Multiple (LCM) of 10, 11 and 12?

Answer

LCM of 10, 11 and 12 is
660

(Six hundred sixty)

660 is the smallest positive integer that 10, 11 and 12 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 11 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 10: 2 × 5 (exponent form: 2 × 5)

All Prime Factors of 11: 11 (exponent form: 11)

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

Prime factor101112Highest power
22—2222
3——33
55——5
11—11—11

LCM = 22 × 3 × 5 × 11 = 660

Checking the LCM of 10, 11 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(10, 11) = (10 × 11) ÷ 1 = 110 ÷ 1 = 110

LCM(110, 12) = (110 × 12) ÷ 2 = 1,320 ÷ 2 = 660

LCM(10, 11, 12) = 660

The pairs may be taken in any order — 11 and 12 first, then 10 — and the answer is the same 660. 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 10, 11 and 12? (The answer is: 660). Enter the first number (e.g. '10'), the second (e.g. '11') 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
11011110
21011110
31011330
41011220
51011110
61011330
71011770
81011440
91011990
101011110
101111110
101112660
1011131,430
101114770
101115330
101116880
1011171,870
101118990
1011192,090
101120220
1011212,310
101122110
1011232,530
1011241,320
101125550
1011261,430
1011272,970
1011281,540
1011293,190
101130330

FAQ

What's the Least Common Multiple (LCM) of 10, 11 and 12?

LCM of 10, 11 and 12 is 660

How to find the LCM of 10, 11 and 12 by prime factorization?

Take every prime that appears in 10, 11 and 12 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 11 = 660.

Can you get the LCM of 10, 11 and 12 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 10 and 11 is 110, and the LCM of 110 and 12 is 660 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 660 divisible by 10, 11 and 12?

Yes, and by definition it is the smallest positive integer that is: 660 ÷ 10, 660 ÷ 11 and 660 ÷ 12 all come out whole. Any other common multiple of 10, 11 and 12 is a multiple of 660.

See Also