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    LCM for 8, 10 and 15

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

    What's the Least Common Multiple (LCM) of 8, 10 and 15?

    Answer

    LCM of 8, 10 and 15 is
    120

    (One hundred twenty)

    120 is the smallest positive integer that 8, 10 and 15 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 10 and 15 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 10: 2 × 5 (exponent form: 2 × 5)

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

    Prime factor81015Highest power
    2232—23
    3——33
    5—555

    LCM = 23 × 3 × 5 = 120

    Checking the LCM of 8, 10 and 15 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, 10) = (8 × 10) ÷ 2 = 80 ÷ 2 = 40

    LCM(40, 15) = (40 × 15) ÷ 5 = 600 ÷ 5 = 120

    LCM(8, 10, 15) = 120

    The pairs may be taken in any order — 10 and 15 first, then 8 — and the answer is the same 120. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 8, 10 and 15?. The LCM of 8, 10 and 15 is 120 — 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
    181040
    281040
    3810120
    481040
    581040
    6810120
    7810280
    881040
    8910360
    8101040
    81011440
    81012120
    81013520
    81014280
    81015120
    8101680
    81017680
    81018360
    81019760
    8102040
    81021840
    81022440
    81023920
    81024120
    81025200
    81026520
    810271,080
    81028280
    810291,160
    81030120

    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, 10 and 15? (The answer is: 120). Enter the first number (e.g. '8'), the second (e.g. '10') and the third (e.g. '15'), 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, 10 and 15?

    LCM of 8, 10 and 15 is 120

    How to find the LCM of 8, 10 and 15 by prime factorization?

    Take every prime that appears in 8, 10 and 15 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

    Can you get the LCM of 8, 10 and 15 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 10 is 40, and the LCM of 40 and 15 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 120 divisible by 8, 10 and 15?

    Yes, and by definition it is the smallest positive integer that is: 120 ÷ 8, 120 ÷ 10 and 120 ÷ 15 all come out whole. Any other common multiple of 8, 10 and 15 is a multiple of 120.

    See Also