LCM for 18, 20 and 36

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 18, 20 and 36?

Answer

LCM of 18, 20 and 36 is
180

(One hundred eighty)

180 is the smallest positive integer that 18, 20 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 18, 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

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 factor182036Highest power
22222222
332—3232
5—5—5

LCM = 22 × 32 × 5 = 180

Checking the LCM of 18, 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(18, 20) = (18 × 20) ÷ 2 = 360 ÷ 2 = 180

LCM(180, 36) = (180 × 36) ÷ 36 = 6,480 ÷ 36 = 180

LCM(18, 20, 36) = 180

The pairs may be taken in any order — 20 and 36 first, then 18 — and the answer is the same 180. That is exactly why the two routes on this page agree.

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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 18, 20 and 36? (The answer is: 180). Enter the first number (e.g. '18'), 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
1820211,260
1820221,980
1820234,140
182024360
182025900
1820262,340
182027540
1820281,260
1820295,220
182030180
1820315,580
1820321,440
1820331,980
1820343,060
1820351,260
182036180
1820376,660
1820383,420
1820392,340
182040360
1820417,380
1820421,260
1820437,740
1820441,980
182045180
1820464,140
1820478,460
182048720
1820498,820
182050900

FAQ

What's the Least Common Multiple (LCM) of 18, 20 and 36?

LCM of 18, 20 and 36 is 180

How to find the LCM of 18, 20 and 36 by prime factorization?

Take every prime that appears in 18, 20 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 18, 20 and 36 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 18 and 20 is 180, and the LCM of 180 and 36 is 180 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 180 divisible by 18, 20 and 36?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 18, 180 ÷ 20 and 180 ÷ 36 all come out whole. Any other common multiple of 18, 20 and 36 is a multiple of 180.

See Also