LCM for 10, 18 and 20

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

What's the Least Common Multiple (LCM) of 10, 18 and 20?

Answer

LCM of 10, 18 and 20 is
180

(One hundred eighty)

180 is the smallest positive integer that 10, 18 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 18 and 20 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 10: 2 × 5 (exponent form: 2 × 5)

All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

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

Prime factor101820Highest power
2222222
3—32—32
55—55

LCM = 22 × 32 × 5 = 180

Checking the LCM of 10, 18 and 20 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(10, 18) = (10 × 18) ÷ 2 = 180 ÷ 2 = 90

LCM(90, 20) = (90 × 20) ÷ 10 = 1,800 ÷ 10 = 180

LCM(10, 18, 20) = 180

The pairs may be taken in any order — 18 and 20 first, then 10 — 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 10, 18 and 20? (The answer is: 180). Enter the first number (e.g. '10'), the second (e.g. '18') and the third (e.g. '20'), 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
5101890
6101890
71018630
81018360
9101890
10101890
101118990
101218180
1013181,170
101418630
10151890
101618720
1017181,530
10181890
1018191,710
101820180
101821630
101822990
1018232,070
101824360
101825450
1018261,170
101827270
1018281,260
1018292,610
10183090
1018312,790
1018321,440
101833990
1018341,530

FAQ

What's the Least Common Multiple (LCM) of 10, 18 and 20?

LCM of 10, 18 and 20 is 180

How to find the LCM of 10, 18 and 20 by prime factorization?

Take every prime that appears in 10, 18 and 20 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 10, 18 and 20 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 10 and 18 is 90, and the LCM of 90 and 20 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 10, 18 and 20?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 10, 180 ÷ 18 and 180 ÷ 20 all come out whole. Any other common multiple of 10, 18 and 20 is a multiple of 180.

See Also