LCM for 20, 24 and 28

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What's the Least Common Multiple (LCM) of 20, 24 and 28?

Answer

LCM of 20, 24 and 28 is
840

First common multiples: 840; 1,680; 2,520; …

840 is divisible by all three: 840 ÷ 20 = 42, 840 ÷ 24 = 35, 840 ÷ 28 = 30 — and 42, 35 and 30 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 42 and of y/24 by 35 and of z/28 by 30.

20 = 22 × 5

24 = 23 × 3

28 = 22 × 7

Prime202428Highest power
222232223
3—3—3
55——5
7——77

— = 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 × 7 = 840

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LCM Table

1st2nd3rdLCM
1320241,560
142024840
152024120
162024240
1720242,040
182024360
1920242,280
202024120
202124840
2022241,320
2023242,760
202424120
202425600
2024261,560
2024271,080
202428840
2024293,480
202430120
2024313,720
202432480
2024331,320
2024342,040
202435840
202436360
2024374,440
2024382,280
2024391,560
202440120
2024414,920
202442840

FAQ

What's the Least Common Multiple (LCM) of 20, 24 and 28?

LCM of 20, 24 and 28 is 840

How to find the LCM of 20, 24 and 28 by prime factorization?

Take every prime that appears in 20, 24 and 28 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 × 7 = 840.

Can you get the LCM of 20, 24 and 28 two numbers at a time?

Yes. The LCM of 20 and 24 is 120, and the LCM of 120 and 28 is 840 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 840 divisible by 20, 24 and 28?

Yes, and by definition it is the smallest positive integer that is: 840 ÷ 20, 840 ÷ 24 and 840 ÷ 28 all come out whole. Any other common multiple of 20, 24 and 28 is a multiple of 840.

See Also