LCM for 10, 18 and 27

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

What's the Least Common Multiple (LCM) of 10, 18 and 27?

Answer

LCM of 10, 18 and 27 is
270

(Two hundred seventy)

270 is the smallest positive integer that 10, 18 and 27 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 18 and 27 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 27: 3 × 3 × 3 (exponent form: 33)

Prime factor101827Highest power
222—2
3—323333
55——5

LCM = 2 × 33 × 5 = 270

Checking the LCM of 10, 18 and 27 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, 27) = (90 × 27) ÷ 9 = 2,430 ÷ 9 = 270

LCM(10, 18, 27) = 270

The pairs may be taken in any order — 18 and 27 first, then 10 — and the answer is the same 270. That is exactly why the two routes on this page agree.

Related Calculations

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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 27? (The answer is: 270). Enter the first number (e.g. '10'), the second (e.g. '18') and the third (e.g. '27'), 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
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
101835630
101836180
1018373,330
1018381,710
1018391,170
101840360
1018413,690

FAQ

What's the Least Common Multiple (LCM) of 10, 18 and 27?

LCM of 10, 18 and 27 is 270

How to find the LCM of 10, 18 and 27 by prime factorization?

Take every prime that appears in 10, 18 and 27 to the highest power it reaches in any one of them and multiply: 2 × 3³ × 5 = 270.

Can you get the LCM of 10, 18 and 27 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 27 is 270 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 270 divisible by 10, 18 and 27?

Yes, and by definition it is the smallest positive integer that is: 270 ÷ 10, 270 ÷ 18 and 270 ÷ 27 all come out whole. Any other common multiple of 10, 18 and 27 is a multiple of 270.

See Also