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    LCM for 15, 30 and 90

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

    What's the Least Common Multiple (LCM) of 15, 30 and 90?

    Answer

    LCM of 15, 30 and 90 is
    90

    (Ninety)

    90 is the smallest positive integer that 15, 30 and 90 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 15, 30 and 90 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 15: 3 × 5 (exponent form: 3 × 5)

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

    All Prime Factors of 90: 2 × 3 × 3 × 5 (exponent form: 2 × 32 × 5)

    Prime factor153090Highest power
    2—222
    3333232
    55555

    LCM = 2 × 32 × 5 = 90

    Checking the LCM of 15, 30 and 90 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(15, 30) = (15 × 30) ÷ 15 = 450 ÷ 15 = 30

    LCM(30, 90) = (30 × 90) ÷ 30 = 2,700 ÷ 30 = 90

    LCM(15, 30, 90) = 90

    The pairs may be taken in any order — 30 and 90 first, then 15 — and the answer is the same 90. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 15, 30 and 90?. The LCM of 15, 30 and 90 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
    153075150
    1530761,140
    1530772,310
    153078390
    1530792,370
    153080240
    153081810
    1530821,230
    1530832,490
    153084420
    153085510
    1530861,290
    153087870
    1530881,320
    1530892,670
    15309090
    1530912,730
    1530921,380
    153093930
    1530941,410
    153095570
    153096480
    1530972,910
    1530981,470
    153099990
    1530100300
    15301013,030
    1530102510
    15301033,090
    15301041,560

    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 15, 30 and 90? (The answer is: 90). Enter the first number (e.g. '15'), the second (e.g. '30') and the third (e.g. '90'), 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 15, 30 and 90?

    LCM of 15, 30 and 90 is 90

    How to find the LCM of 15, 30 and 90 by prime factorization?

    Take every prime that appears in 15, 30 and 90 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

    Can you get the LCM of 15, 30 and 90 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 15 and 30 is 30, and the LCM of 30 and 90 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 15, 30 and 90?

    Yes, and by definition it is the smallest positive integer that is: 90 ÷ 15, 90 ÷ 30 and 90 ÷ 90 all come out whole. Any other common multiple of 15, 30 and 90 is a multiple of 90.

    See Also