LCM for 6, 18 and 45

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

What's the Least Common Multiple (LCM) of 6, 18 and 45?

Answer

LCM of 6, 18 and 45 is
90

(Ninety)

90 is the smallest positive integer that 6, 18 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 6, 18 and 45 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 6: 2 × 3 (exponent form: 2 × 3)

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

All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

Prime factor61845Highest power
222—2
33323232
5——55

LCM = 2 × 32 × 5 = 90

Checking the LCM of 6, 18 and 45 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(6, 18) = (6 × 18) ÷ 6 = 108 ÷ 6 = 18

LCM(18, 45) = (18 × 45) ÷ 9 = 810 ÷ 9 = 90

LCM(6, 18, 45) = 90

The pairs may be taken in any order — 18 and 45 first, then 6 — and the answer is the same 90. 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 6, 18 and 45? (The answer is: 90). Enter the first number (e.g. '6'), the second (e.g. '18') and the third (e.g. '45'), 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
6183090
61831558
61832288
61833198
61834306
61835630
6183636
61837666
61838342
61839234
61840360
61841738
61842126
61843774
61844396
6184590
61846414
61847846
61848144
61849882
61850450
61851306
61852468
61853954
6185454
61855990
61856504
61857342
61858522
618591,062

FAQ

What's the Least Common Multiple (LCM) of 6, 18 and 45?

LCM of 6, 18 and 45 is 90

How to find the LCM of 6, 18 and 45 by prime factorization?

Take every prime that appears in 6, 18 and 45 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

Can you get the LCM of 6, 18 and 45 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 6 and 18 is 18, and the LCM of 18 and 45 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 6, 18 and 45?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 6, 90 ÷ 18 and 90 ÷ 45 all come out whole. Any other common multiple of 6, 18 and 45 is a multiple of 90.

See Also