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    LCM for 10, 15 and 30

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

    What's the Least Common Multiple (LCM) of 10, 15 and 30?

    Answer

    LCM of 10, 15 and 30 is
    30

    (Thirty)

    30 is the smallest positive integer that 10, 15 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 10, 15 and 30 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 10: 2 × 5 (exponent form: 2 × 5)

    All Prime Factors of 15: 3 × 5 (exponent form: 3 × 5)

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

    Prime factor101530Highest power
    22—22
    3—333
    55555

    LCM = 2 × 3 × 5 = 30

    Checking the LCM of 10, 15 and 30 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(10, 15) = (10 × 15) ÷ 5 = 150 ÷ 5 = 30

    LCM(30, 30) = (30 × 30) ÷ 30 = 900 ÷ 30 = 30

    LCM(10, 15, 30) = 30

    The pairs may be taken in any order — 15 and 30 first, then 10 — and the answer is the same 30. That is exactly why the two routes on this page agree.

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    What is the LCM of 10, 15 and 30?. The LCM of 10, 15 and 30 is 30 — 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
    10151530
    101516240
    101517510
    10151890
    101519570
    10152060
    101521210
    101522330
    101523690
    101524120
    101525150
    101526390
    101527270
    101528420
    101529870
    10153030
    101531930
    101532480
    101533330
    101534510
    101535210
    101536180
    1015371,110
    101538570
    101539390
    101540120
    1015411,230
    101542210
    1015431,290
    101544660

    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 10, 15 and 30? (The answer is: 30). Enter the first number (e.g. '10'), the second (e.g. '15') and the third (e.g. '30'), 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 10, 15 and 30?

    LCM of 10, 15 and 30 is 30

    How to find the LCM of 10, 15 and 30 by prime factorization?

    Take every prime that appears in 10, 15 and 30 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5 = 30.

    Can you get the LCM of 10, 15 and 30 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 10 and 15 is 30, and the LCM of 30 and 30 is 30 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 30 divisible by 10, 15 and 30?

    Yes, and by definition it is the smallest positive integer that is: 30 ÷ 10, 30 ÷ 15 and 30 ÷ 30 all come out whole. Any other common multiple of 10, 15 and 30 is a multiple of 30.

    See Also