LCM for 35, 40 and 120

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What's the Least Common Multiple (LCM) of 35, 40 and 120?

Answer

LCM of 35, 40 and 120 is
840

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

840 is divisible by all three: 840 ÷ 35 = 24, 840 ÷ 40 = 21, 840 ÷ 120 = 7 — and 24, 21 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/35 by 24 and of y/40 by 21 and of z/120 by 7.

35 = 5 × 7

40 = 23 × 5

120 = 23 × 3 × 5

Prime3540120Highest power
2—232323
3——33
55555
77——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
3540105840
354010614,840
354010729,960
35401087,560
354010930,520
35401103,080
354011131,080
3540112560
354011331,640
354011415,960
35401156,440
35401168,120
354011732,760
354011816,520
35401194,760
3540120840
354012133,880
354012217,080
354012334,440
35401248,680
35401257,000
35401262,520
354012735,560
35401284,480
354012936,120
35401303,640
354013136,680
35401329,240
35401335,320
354013418,760

FAQ

What's the Least Common Multiple (LCM) of 35, 40 and 120?

LCM of 35, 40 and 120 is 840

How to find the LCM of 35, 40 and 120 by prime factorization?

Take every prime that appears in 35, 40 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 35, 40 and 120 two numbers at a time?

Yes. The LCM of 35 and 40 is 280, and the LCM of 280 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 35, 40 and 120?

Yes, and by definition it is the smallest positive integer that is: 840 ÷ 35, 840 ÷ 40 and 840 ÷ 120 all come out whole. Any other common multiple of 35, 40 and 120 is a multiple of 840.

See Also