LCM for 6, 8 and 15

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What's the Least Common Multiple (LCM) of 6, 8 and 15?

Answer

LCM of 6, 8 and 15 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 6 = 20, 120 ÷ 8 = 15, 120 ÷ 15 = 8 — and 20, 15 and 8 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/6 by 20 and of y/8 by 15 and of z/15 by 8.

6 = 2 × 3

8 = 23

15 = 3 × 5

Prime6815Highest power
2223—23
33—33
5——55

— = 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
16824
26824
36824
46824
568120
66824
678168
68824
68972
6810120
6811264
681224
6813312
6814168
6815120
681648
6817408
681872
6819456
6820120
6821168
6822264
6823552
682424
6825600
6826312
6827216
6828168
6829696
6830120

FAQ

What's the Least Common Multiple (LCM) of 6, 8 and 15?

LCM of 6, 8 and 15 is 120

How to find the LCM of 6, 8 and 15 by prime factorization?

Take every prime that appears in 6, 8 and 15 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 6, 8 and 15 two numbers at a time?

Yes. The LCM of 6 and 8 is 24, and the LCM of 24 and 15 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 6, 8 and 15?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 6, 120 ÷ 8 and 120 ÷ 15 all come out whole. Any other common multiple of 6, 8 and 15 is a multiple of 120.

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