LCM for 8, 20 and 36

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

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

Answer

LCM of 8, 20 and 36 is
360

(Three hundred sixty)

360 is the smallest positive integer that 8, 20 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 20 and 36 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

Prime factor82036Highest power
223222223
3——3232
5—5—5

LCM = 23 × 32 × 5 = 360

Checking the LCM of 8, 20 and 36 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(8, 20) = (8 × 20) ÷ 4 = 160 ÷ 4 = 40

LCM(40, 36) = (40 × 36) ÷ 4 = 1,440 ÷ 4 = 360

LCM(8, 20, 36) = 360

The pairs may be taken in any order — 20 and 36 first, then 8 — and the answer is the same 360. That is exactly why the two routes on this page agree.

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See Also

About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 8, 20 and 36? (The answer is: 360). Enter the first number (e.g. '8'), the second (e.g. '20') and the third (e.g. '36'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
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, and it is the check this page prints. 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.

See Also