LCM for 108, 120 and 132

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 108, 120 and 132?

Answer

LCM of 108, 120 and 132 is
11,880

(Eleven thousand eight hundred eighty)

11,880 is the smallest positive integer that 108, 120 and 132 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 108, 120 and 132 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 108: 2 × 2 × 3 × 3 × 3 (exponent form: 22 × 33)

All Prime Factors of 120: 2 × 2 × 2 × 3 × 5 (exponent form: 23 × 3 × 5)

All Prime Factors of 132: 2 × 2 × 3 × 11 (exponent form: 22 × 3 × 11)

Prime factor108120132Highest power
222232223
3333333
5—5—5
11——1111

LCM = 23 × 33 × 5 × 11 = 11,880

Checking the LCM of 108, 120 and 132 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(108, 120) = (108 × 120) ÷ 12 = 12,960 ÷ 12 = 1,080

LCM(1,080, 132) = (1,080 × 132) ÷ 12 = 142,560 ÷ 12 = 11,880

LCM(108, 120, 132) = 11,880

The pairs may be taken in any order — 120 and 132 first, then 108 — and the answer is the same 11,880. That is exactly why the two routes on this page agree.

Related Calculations

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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 108, 120 and 132? (The answer is: 11,880). Enter the first number (e.g. '108'), the second (e.g. '120') and the third (e.g. '132'), 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
10811712014,040
10811812063,720
108119120128,520
1081201201,080
108120121130,680
10812012265,880
10812012344,280
10812012433,480
10812012527,000
1081201267,560
108120127137,160
10812012817,280
10812012946,440
10812013014,040
108120131141,480
10812013211,880
108120133143,640
10812013472,360
1081201351,080
10812013618,360
108120137147,960
10812013824,840
108120139150,120
1081201407,560
10812014150,760
10812014276,680
108120143154,440
1081201442,160
10812014531,320
10812014678,840

FAQ

What's the Least Common Multiple (LCM) of 108, 120 and 132?

LCM of 108, 120 and 132 is 11,880

How to find the LCM of 108, 120 and 132 by prime factorization?

Take every prime that appears in 108, 120 and 132 to the highest power it reaches in any one of them and multiply: 2³ × 3³ × 5 × 11 = 11,880.

Can you get the LCM of 108, 120 and 132 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 108 and 120 is 1,080, and the LCM of 1,080 and 132 is 11,880 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 11,880 divisible by 108, 120 and 132?

Yes, and by definition it is the smallest positive integer that is: 11,880 ÷ 108, 11,880 ÷ 120 and 11,880 ÷ 132 all come out whole. Any other common multiple of 108, 120 and 132 is a multiple of 11,880.

See Also