LCM for 3, 10 and 18

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

What's the Least Common Multiple (LCM) of 3, 10 and 18?

Answer

LCM of 3, 10 and 18 is
90

(Ninety)

90 is the smallest positive integer that 3, 10 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 3, 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 3: 3 (exponent form: 3)

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

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

Prime factor31018Highest power
2—222
33—3232
5—5—5

LCM = 2 × 32 × 5 = 90

Checking the LCM of 3, 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(3, 10) = (3 × 10) ÷ 1 = 30 ÷ 1 = 30

LCM(30, 18) = (30 × 18) ÷ 6 = 540 ÷ 6 = 90

LCM(3, 10, 18) = 90

The pairs may be taken in any order — 10 and 18 first, then 3 — and the answer is the same 90. That is exactly why the two routes on this page agree.

Related Calculations

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 3, 10 and 18? (The answer is: 90). Enter the first number (e.g. '3'), 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
331030
341060
351030
361030
3710210
3810120
391090
3101030
31011330
3101260
31013390
31014210
3101530
31016240
31017510
3101890
31019570
3102060
31021210
31022330
31023690
31024120
31025150
31026390
31027270
31028420
31029870
3103030
31031930
31032480

FAQ

What's the Least Common Multiple (LCM) of 3, 10 and 18?

LCM of 3, 10 and 18 is 90

How to find the LCM of 3, 10 and 18 by prime factorization?

Take every prime that appears in 3, 10 and 18 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

Can you get the LCM of 3, 10 and 18 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 3 and 10 is 30, and the LCM of 30 and 18 is 90 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 90 divisible by 3, 10 and 18?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 3, 90 ÷ 10 and 90 ÷ 18 all come out whole. Any other common multiple of 3, 10 and 18 is a multiple of 90.

See Also