LCM for 8, 20 and 24

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What's the Least Common Multiple (LCM) of 8, 20 and 24?

Answer

LCM of 8, 20 and 24 is
120

First common multiples: 120, 240, 360, …

120 is divisible by all three: 120 ÷ 8 = 15, 120 ÷ 20 = 6, 120 ÷ 24 = 5 — and 15, 6 and 5 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 15 and of y/20 by 6 and of z/24 by 5.

8 = 23

20 = 22 × 5

24 = 23 × 3

Prime82024Highest power
223222323
3——33
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 × 3 × 5 = 120

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LCM Table

1st2nd3rdLCM
8920360
8102040
81120440
81220120
81320520
81420280
81520120
8162080
81720680
81820360
81920760
8202040
82021840
82022440
82023920
82024120
82025200
82026520
820271,080
82028280
820291,160
82030120
820311,240
82032160
820331,320
82034680
82035280
82036360
820371,480
82038760

FAQ

What's the Least Common Multiple (LCM) of 8, 20 and 24?

LCM of 8, 20 and 24 is 120

How to find the LCM of 8, 20 and 24 by prime factorization?

Take every prime that appears in 8, 20 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

Can you get the LCM of 8, 20 and 24 two numbers at a time?

Yes. The LCM of 8 and 20 is 40, and the LCM of 40 and 24 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 8, 20 and 24?

Yes, and by definition it is the smallest positive integer that is: 120 ÷ 8, 120 ÷ 20 and 120 ÷ 24 all come out whole. Any other common multiple of 8, 20 and 24 is a multiple of 120.

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