LCM for 9, 10 and 18

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

What's the Least Common Multiple (LCM) of 9, 10 and 18?

Answer

LCM of 9, 10 and 18 is
90

(Ninety)

90 is the smallest positive integer that 9, 10 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 9, 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 9: 3 × 3 (exponent form: 32)

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

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

Prime factor91018Highest power
2—222
332—3232
5—5—5

LCM = 2 × 32 × 5 = 90

Checking the LCM of 9, 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(9, 10) = (9 × 10) ÷ 1 = 90 ÷ 1 = 90

LCM(90, 18) = (90 × 18) ÷ 18 = 1,620 ÷ 18 = 90

LCM(9, 10, 18) = 90

The pairs may be taken in any order — 10 and 18 first, then 9 — 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 9, 10 and 18? (The answer is: 90). Enter the first number (e.g. '9'), 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
391090
4910180
591090
691090
7910630
8910360
991090
9101090
91011990
91012180
910131,170
91014630
9101590
91016720
910171,530
9101890
910191,710
91020180
91021630
91022990
910232,070
91024360
91025450
910261,170
91027270
910281,260
910292,610
9103090
910312,790
910321,440

FAQ

What's the Least Common Multiple (LCM) of 9, 10 and 18?

LCM of 9, 10 and 18 is 90

How to find the LCM of 9, 10 and 18 by prime factorization?

Take every prime that appears in 9, 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 9, 10 and 18 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 9 and 10 is 90, and the LCM of 90 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 9, 10 and 18?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 9, 90 ÷ 10 and 90 ÷ 18 all come out whole. Any other common multiple of 9, 10 and 18 is a multiple of 90.

See Also