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    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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    What is the LCM of 6, 18 and 45?. The LCM of 6, 18 and 45 is 90 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
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    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

    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

    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