LCM for 20, 24 and 45

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What's the Least Common Multiple (LCM) of 20, 24 and 45?

Answer

LCM of 20, 24 and 45 is
360

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

360 is divisible by all three: 360 ÷ 20 = 18, 360 ÷ 24 = 15, 360 ÷ 45 = 8 — and 18, 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/20 by 18 and of y/24 by 15 and of z/45 by 8.

20 = 22 × 5

24 = 23 × 3

45 = 32 × 5

Prime202445Highest power
22223—23
3—33232
55—55

— = 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
202430120
2024313,720
202432480
2024331,320
2024342,040
202435840
202436360
2024374,440
2024382,280
2024391,560
202440120
2024414,920
202442840
2024435,160
2024441,320
202445360
2024462,760
2024475,640
202448240
2024495,880
202450600
2024512,040
2024521,560
2024536,360
2024541,080
2024551,320
202456840
2024572,280
2024583,480
2024597,080

FAQ

What's the Least Common Multiple (LCM) of 20, 24 and 45?

LCM of 20, 24 and 45 is 360

How to find the LCM of 20, 24 and 45 by prime factorization?

Take every prime that appears in 20, 24 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 20, 24 and 45 two numbers at a time?

Yes. The LCM of 20 and 24 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 20, 24 and 45?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 20, 360 ÷ 24 and 360 ÷ 45 all come out whole. Any other common multiple of 20, 24 and 45 is a multiple of 360.

See Also