LCM for 108, 120 and 132

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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

First common multiples: 11,880; 23,760; 35,640; …

11,880 is divisible by all three: 11,880 ÷ 108 = 110; 11,880 ÷ 120 = 99; 11,880 ÷ 132 = 90 — and 110, 99 and 90 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/108 by 110 and of y/120 by 99 and of z/132 by 90.

108 = 22 × 33

120 = 23 × 3 × 5

132 = 22 × 3 × 11

Prime108120132Highest power
222232223
3333333
5—5—5
11——1111

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 23 × 33 × 5 × 11 = 11,880

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LCM Table

1st2nd3rdLCM
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. 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