LCM for 4, 10 and 18

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

What's the Least Common Multiple (LCM) of 4, 10 and 18?

Answer

LCM of 4, 10 and 18 is
180

(One hundred eighty)

180 is the smallest positive integer that 4, 10 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 4, 10 and 18 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 4: 2 × 2 (exponent form: 22)

All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

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

Prime factor41018Highest power
2222222
3——3232
5—5—5

LCM = 22 × 32 × 5 = 180

Checking the LCM of 4, 10 and 18 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(4, 10) = (4 × 10) ÷ 2 = 40 ÷ 2 = 20

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

LCM(4, 10, 18) = 180

The pairs may be taken in any order — 10 and 18 first, then 4 — 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 4, 10 and 18? (The answer is: 180). Enter the first number (e.g. '4'), the second (e.g. '10') and the third (e.g. '18'), 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
341060
441020
451020
461060
4710140
481040
4910180
4101020
41011220
4101260
41013260
41014140
4101560
4101680
41017340
41018180
41019380
4102020
41021420
41022220
41023460
41024120
41025100
41026260
41027540
41028140
41029580
4103060
41031620
41032160

FAQ

What's the Least Common Multiple (LCM) of 4, 10 and 18?

LCM of 4, 10 and 18 is 180

How to find the LCM of 4, 10 and 18 by prime factorization?

Take every prime that appears in 4, 10 and 18 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 4, 10 and 18 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 4 and 10 is 20, and the LCM of 20 and 18 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 4, 10 and 18?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 4, 180 ÷ 10 and 180 ÷ 18 all come out whole. Any other common multiple of 4, 10 and 18 is a multiple of 180.

See Also