LCM for 10, 15 and 24

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What's the Least Common Multiple (LCM) of 10, 15 and 24?

Answer

LCM of 10, 15 and 24 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 10 = 12, 120 ÷ 15 = 8, 120 ÷ 24 = 5 — and 12, 8 and 5 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/10 by 12 and of y/15 by 8 and of z/24 by 5.

10 = 2 × 5

15 = 3 × 5

24 = 23 × 3

Prime101524Highest power
22—2323
3—333
555—5

— = 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
9101590
10101530
101115330
10121560
101315390
101415210
10151530
101516240
101517510
10151890
101519570
10152060
101521210
101522330
101523690
101524120
101525150
101526390
101527270
101528420
101529870
10153030
101531930
101532480
101533330
101534510
101535210
101536180
1015371,110
101538570

FAQ

What's the Least Common Multiple (LCM) of 10, 15 and 24?

LCM of 10, 15 and 24 is 120

How to find the LCM of 10, 15 and 24 by prime factorization?

Take every prime that appears in 10, 15 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 10, 15 and 24 two numbers at a time?

Yes. The LCM of 10 and 15 is 30, and the LCM of 30 and 24 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 10, 15 and 24?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 10, 120 ÷ 15 and 120 ÷ 24 all come out whole. Any other common multiple of 10, 15 and 24 is a multiple of 120.

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