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    LCM for 8, 30 and 45

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

    What's the Least Common Multiple (LCM) of 8, 30 and 45?

    Answer

    LCM of 8, 30 and 45 is
    360

    (Three hundred sixty)

    360 is the smallest positive integer that 8, 30 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 30 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 8: 2 × 2 × 2 (exponent form: 23)

    All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

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

    Prime factor83045Highest power
    2232—23
    3—33232
    5—555

    LCM = 23 × 32 × 5 = 360

    Checking the LCM of 8, 30 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(8, 30) = (8 × 30) ÷ 2 = 240 ÷ 2 = 120

    LCM(120, 45) = (120 × 45) ÷ 15 = 5,400 ÷ 15 = 360

    LCM(8, 30, 45) = 360

    The pairs may be taken in any order — 30 and 45 first, then 8 — and the answer is the same 360. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 8, 30 and 45?. The LCM of 8, 30 and 45 is 360 — 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
    83030120
    830313,720
    83032480
    830331,320
    830342,040
    83035840
    83036360
    830374,440
    830382,280
    830391,560
    83040120
    830414,920
    83042840
    830435,160
    830441,320
    83045360
    830462,760
    830475,640
    83048240
    830495,880
    83050600
    830512,040
    830521,560
    830536,360
    830541,080
    830551,320
    83056840
    830572,280
    830583,480
    830597,080

    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 8, 30 and 45? (The answer is: 360). Enter the first number (e.g. '8'), the second (e.g. '30') 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 8, 30 and 45?

    LCM of 8, 30 and 45 is 360

    How to find the LCM of 8, 30 and 45 by prime factorization?

    Take every prime that appears in 8, 30 and 45 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

    Can you get the LCM of 8, 30 and 45 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 30 is 120, and the LCM of 120 and 45 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 360 divisible by 8, 30 and 45?

    Yes, and by definition it is the smallest positive integer that is: 360 ÷ 8, 360 ÷ 30 and 360 ÷ 45 all come out whole. Any other common multiple of 8, 30 and 45 is a multiple of 360.

    See Also