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    LCM for 5, 8 and 15

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

    What's the Least Common Multiple (LCM) of 5, 8 and 15?

    Answer

    LCM of 5, 8 and 15 is
    120

    (One hundred twenty)

    120 is the smallest positive integer that 5, 8 and 15 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 5, 8 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 5: 5 (exponent form: 5)

    All Prime Factors of 8: 2 × 2 × 2 (exponent form: 23)

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

    Prime factor5815Highest power
    2—23—23
    3——33
    55—55

    LCM = 23 × 3 × 5 = 120

    Checking the LCM of 5, 8 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(5, 8) = (5 × 8) ÷ 1 = 40 ÷ 1 = 40

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

    LCM(5, 8, 15) = 120

    The pairs may be taken in any order — 8 and 15 first, then 5 — and the answer is the same 120. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 5, 8 and 15?. The LCM of 5, 8 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
    15840
    25840
    358120
    45840
    55840
    568120
    578280
    58840
    589360
    581040
    5811440
    5812120
    5813520
    5814280
    5815120
    581680
    5817680
    5818360
    5819760
    582040
    5821840
    5822440
    5823920
    5824120
    5825200
    5826520
    58271,080
    5828280
    58291,160
    5830120

    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 5, 8 and 15? (The answer is: 120). Enter the first number (e.g. '5'), the second (e.g. '8') 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 5, 8 and 15?

    LCM of 5, 8 and 15 is 120

    How to find the LCM of 5, 8 and 15 by prime factorization?

    Take every prime that appears in 5, 8 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 5, 8 and 15 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 5 and 8 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 5, 8 and 15?

    Yes, and by definition it is the smallest positive integer that is: 120 ÷ 5, 120 ÷ 8 and 120 ÷ 15 all come out whole. Any other common multiple of 5, 8 and 15 is a multiple of 120.

    See Also