LCM for 15, 40 and 60

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What's the Least Common Multiple (LCM) of 15, 40 and 60?

Answer

LCM of 15, 40 and 60 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 15 = 8, 120 ÷ 40 = 3, 120 ÷ 60 = 2 — and 8, 3 and 2 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/15 by 8 and of y/40 by 3 and of z/60 by 2.

15 = 3 × 5

40 = 23 × 5

60 = 22 × 3 × 5

Prime154060Highest power
2—232223
33—33
55555

— = 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 = 120

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LCM Table

1st2nd3rdLCM
154045360
1540462,760
1540475,640
154048240
1540495,880
154050600
1540512,040
1540521,560
1540536,360
1540541,080
1540551,320
154056840
1540572,280
1540583,480
1540597,080
154060120
1540617,320
1540623,720
1540632,520
154064960
1540651,560
1540661,320
1540678,040
1540682,040
1540692,760
154070840
1540718,520
154072360
1540738,760
1540744,440

FAQ

What's the Least Common Multiple (LCM) of 15, 40 and 60?

LCM of 15, 40 and 60 is 120

How to find the LCM of 15, 40 and 60 by prime factorization?

Take every prime that appears in 15, 40 and 60 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 15, 40 and 60 two numbers at a time?

Yes. The LCM of 15 and 40 is 120, and the LCM of 120 and 60 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 120 divisible by 15, 40 and 60?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 15, 120 ÷ 40 and 120 ÷ 60 all come out whole. Any other common multiple of 15, 40 and 60 is a multiple of 120.

See Also