LCM for 12, 30 and 84

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What's the Least Common Multiple (LCM) of 12, 30 and 84?

Answer

LCM of 12, 30 and 84 is
420

First common multiples: 420; 840; 1,260; …

420 is divisible by all three: 420 ÷ 12 = 35, 420 ÷ 30 = 14, 420 ÷ 84 = 5 — and 35, 14 and 5 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/12 by 35 and of y/30 by 14 and of z/84 by 5.

12 = 22 × 3

30 = 2 × 3 × 5

84 = 22 × 3 × 7

Prime123084Highest power
22222222
33333
5—5—5
7——77

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

LCM = 22 × 3 × 5 × 7 = 420

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LCM Table

1st2nd3rdLCM
1230691,380
123070420
1230714,260
123072360
1230734,380
1230742,220
123075300
1230761,140
1230774,620
123078780
1230794,740
123080240
1230811,620
1230822,460
1230834,980
123084420
1230851,020
1230862,580
1230871,740
1230881,320
1230895,340
123090180
1230915,460
1230921,380
1230931,860
1230942,820
1230951,140
123096480
1230975,820
1230982,940

FAQ

What's the Least Common Multiple (LCM) of 12, 30 and 84?

LCM of 12, 30 and 84 is 420

How to find the LCM of 12, 30 and 84 by prime factorization?

Take every prime that appears in 12, 30 and 84 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 7 = 420.

Can you get the LCM of 12, 30 and 84 two numbers at a time?

Yes. The LCM of 12 and 30 is 60, and the LCM of 60 and 84 is 420 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 420 divisible by 12, 30 and 84?

Yes, and by definition it is the smallest positive integer that is: 420 ÷ 12, 420 ÷ 30 and 420 ÷ 84 all come out whole. Any other common multiple of 12, 30 and 84 is a multiple of 420.

See Also