LCM for 8, 20 and 36

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What's the Least Common Multiple (LCM) of 8, 20 and 36?

Answer

LCM of 8, 20 and 36 is
360

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

360 is divisible by all three: 360 ÷ 8 = 45, 360 ÷ 20 = 18, 360 ÷ 36 = 10 — and 45, 18 and 10 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/8 by 45 and of y/20 by 18 and of z/36 by 10.

8 = 23

20 = 22 × 5

36 = 22 × 32

Prime82036Highest power
223222223
3——3232
5—5—5

— = 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
82021840
82022440
82023920
82024120
82025200
82026520
820271,080
82028280
820291,160
82030120
820311,240
82032160
820331,320
82034680
82035280
82036360
820371,480
82038760
820391,560
8204040
820411,640
82042840
820431,720
82044440
82045360
82046920
820471,880
82048240
820491,960
82050200

FAQ

What's the Least Common Multiple (LCM) of 8, 20 and 36?

LCM of 8, 20 and 36 is 360

How to find the LCM of 8, 20 and 36 by prime factorization?

Take every prime that appears in 8, 20 and 36 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

Can you get the LCM of 8, 20 and 36 two numbers at a time?

Yes. The LCM of 8 and 20 is 40, and the LCM of 40 and 36 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 8, 20 and 36?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 8, 360 ÷ 20 and 360 ÷ 36 all come out whole. Any other common multiple of 8, 20 and 36 is a multiple of 360.

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