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    LCM for 16, 18 and 45

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

    What's the Least Common Multiple (LCM) of 16, 18 and 45?

    Answer

    LCM of 16, 18 and 45 is
    720

    (Seven hundred twenty)

    720 is the smallest positive integer that 16, 18 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 16, 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

    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 factor161845Highest power
    2242—24
    3—323232
    5——55

    LCM = 24 × 32 × 5 = 720

    Checking the LCM of 16, 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(16, 18) = (16 × 18) ÷ 2 = 288 ÷ 2 = 144

    LCM(144, 45) = (144 × 45) ÷ 9 = 6,480 ÷ 9 = 720

    LCM(16, 18, 45) = 720

    The pairs may be taken in any order — 18 and 45 first, then 16 — and the answer is the same 720. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 16, 18 and 45?. The LCM of 16, 18 and 45 is 720 — 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
    161830720
    1618314,464
    161832288
    1618331,584
    1618342,448
    1618355,040
    161836144
    1618375,328
    1618382,736
    1618391,872
    161840720
    1618415,904
    1618421,008
    1618436,192
    1618441,584
    161845720
    1618463,312
    1618476,768
    161848144
    1618497,056
    1618503,600
    1618512,448
    1618521,872
    1618537,632
    161854432
    1618557,920
    1618561,008
    1618572,736
    1618584,176
    1618598,496

    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 16, 18 and 45? (The answer is: 720). Enter the first number (e.g. '16'), 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 16, 18 and 45?

    LCM of 16, 18 and 45 is 720

    How to find the LCM of 16, 18 and 45 by prime factorization?

    Take every prime that appears in 16, 18 and 45 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 5 = 720.

    Can you get the LCM of 16, 18 and 45 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 16 and 18 is 144, and the LCM of 144 and 45 is 720 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 720 divisible by 16, 18 and 45?

    Yes, and by definition it is the smallest positive integer that is: 720 ÷ 16, 720 ÷ 18 and 720 ÷ 45 all come out whole. Any other common multiple of 16, 18 and 45 is a multiple of 720.

    See Also