LCM for 20, 36 and 48

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What's the Least Common Multiple (LCM) of 20, 36 and 48?

Answer

LCM of 20, 36 and 48 is
720

First common multiples: 720; 1,440; 2,160; …

720 is divisible by all three: 720 ÷ 20 = 36, 720 ÷ 36 = 20, 720 ÷ 48 = 15 — and 36, 20 and 15 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 36 and of y/36 by 20 and of z/48 by 15.

20 = 22 × 5

36 = 22 × 32

48 = 24 × 3

Prime203648Highest power
222222424
3—32332
55——5

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

LCM = 24 × 32 × 5 = 720

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LCM Table

1st2nd3rdLCM
2033361,980
2034363,060
2035361,260
203636180
2036376,660
2036383,420
2036392,340
203640360
2036417,380
2036421,260
2036437,740
2036441,980
203645180
2036464,140
2036478,460
203648720
2036498,820
203650900
2036513,060
2036522,340
2036539,540
203654540
2036551,980
2036562,520
2036573,420
2036585,220
20365910,620
203660180
20366110,980
2036625,580

FAQ

What's the Least Common Multiple (LCM) of 20, 36 and 48?

LCM of 20, 36 and 48 is 720

How to find the LCM of 20, 36 and 48 by prime factorization?

Take every prime that appears in 20, 36 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 5 = 720.

Can you get the LCM of 20, 36 and 48 two numbers at a time?

Yes. The LCM of 20 and 36 is 180, and the LCM of 180 and 48 is 720 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 720 divisible by 20, 36 and 48?

Yes, and by definition it is the smallest positive integer that is: 720 ÷ 20, 720 ÷ 36 and 720 ÷ 48 all come out whole. Any other common multiple of 20, 36 and 48 is a multiple of 720.

See Also