LCM for 20, 30 and 40

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What's the Least Common Multiple (LCM) of 20, 30 and 40?

Answer

LCM of 20, 30 and 40 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 20 = 6, 120 ÷ 30 = 4, 120 ÷ 40 = 3 — and 6, 4 and 3 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 6 and of y/30 by 4 and of z/40 by 3.

20 = 22 × 5

30 = 2 × 3 × 5

40 = 23 × 5

Prime203040Highest power
22222323
3—3—3
55555

— = 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
202530300
202630780
202730540
202830420
2029301,740
20303060
2030311,860
203032480
203033660
2030341,020
203035420
203036180
2030372,220
2030381,140
203039780
203040120
2030412,460
203042420
2030432,580
203044660
203045180
2030461,380
2030472,820
203048240
2030492,940
203050300
2030511,020
203052780
2030533,180
203054540

FAQ

What's the Least Common Multiple (LCM) of 20, 30 and 40?

LCM of 20, 30 and 40 is 120

How to find the LCM of 20, 30 and 40 by prime factorization?

Take every prime that appears in 20, 30 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 20, 30 and 40 two numbers at a time?

Yes. The LCM of 20 and 30 is 60, and the LCM of 60 and 40 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 20, 30 and 40?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 20, 120 ÷ 30 and 120 ÷ 40 all come out whole. Any other common multiple of 20, 30 and 40 is a multiple of 120.

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