LCM for 8, 30 and 45

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What's the Least Common Multiple (LCM) of 8, 30 and 45?

Answer

LCM of 8, 30 and 45 is
360

First common multiples: 360; 720; 1,080; …

360 is divisible by all three: 360 ÷ 8 = 45, 360 ÷ 30 = 12, 360 ÷ 45 = 8 — and 45, 12 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/8 by 45 and of y/30 by 12 and of z/45 by 8.

8 = 23

30 = 2 × 3 × 5

45 = 32 × 5

Prime83045Highest power
2232—23
3—33232
5—555

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

LCM = 23 × 32 × 5 = 360

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LCM Table

1st2nd3rdLCM
83030120
830313,720
83032480
830331,320
830342,040
83035840
83036360
830374,440
830382,280
830391,560
83040120
830414,920
83042840
830435,160
830441,320
83045360
830462,760
830475,640
83048240
830495,880
83050600
830512,040
830521,560
830536,360
830541,080
830551,320
83056840
830572,280
830583,480
830597,080

FAQ

What's the Least Common Multiple (LCM) of 8, 30 and 45?

LCM of 8, 30 and 45 is 360

How to find the LCM of 8, 30 and 45 by prime factorization?

Take every prime that appears in 8, 30 and 45 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

Can you get the LCM of 8, 30 and 45 two numbers at a time?

Yes. The LCM of 8 and 30 is 120, and the LCM of 120 and 45 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 360 divisible by 8, 30 and 45?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 8, 360 ÷ 30 and 360 ÷ 45 all come out whole. Any other common multiple of 8, 30 and 45 is a multiple of 360.

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