LCM for 60, 84 and 120

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What's the Least Common Multiple (LCM) of 60, 84 and 120?

Answer

LCM of 60, 84 and 120 is
840

First common multiples: 840; 1,680; 2,520; …

840 is divisible by all three: 840 ÷ 60 = 14, 840 ÷ 84 = 10, 840 ÷ 120 = 7 — and 14, 10 and 7 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/60 by 14 and of y/84 by 10 and of z/120 by 7.

60 = 22 × 3 × 5

84 = 22 × 3 × 7

120 = 23 × 3 × 5

Prime6084120Highest power
222222323
33333
55—55
7—7—7

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

LCM = 23 × 3 × 5 × 7 = 840

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LCM Table

1st2nd3rdLCM
6084105420
608410622,260
608410744,940
60841083,780
608410945,780
60841104,620
608411115,540
60841121,680
608411347,460
60841147,980
60841159,660
608411612,180
608411716,380
608411824,780
60841197,140
6084120840
608412150,820
608412225,620
608412317,220
608412413,020
608412510,500
60841261,260
608412753,340
608412813,440
608412918,060
60841305,460
608413155,020
60841324,620
60841337,980
608413428,140

FAQ

What's the Least Common Multiple (LCM) of 60, 84 and 120?

LCM of 60, 84 and 120 is 840

How to find the LCM of 60, 84 and 120 by prime factorization?

Take every prime that appears in 60, 84 and 120 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 × 7 = 840.

Can you get the LCM of 60, 84 and 120 two numbers at a time?

Yes. The LCM of 60 and 84 is 420, and the LCM of 420 and 120 is 840 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 840 divisible by 60, 84 and 120?

Yes, and by definition it is the smallest positive integer that is: 840 ÷ 60, 840 ÷ 84 and 840 ÷ 120 all come out whole. Any other common multiple of 60, 84 and 120 is a multiple of 840.

See Also