Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    LCM for 8, 15 and 24

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

    What's the Least Common Multiple (LCM) of 8, 15 and 24?

    Answer

    LCM of 8, 15 and 24 is
    120

    (One hundred twenty)

    120 is the smallest positive integer that 8, 15 and 24 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 15 and 24 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 15: 3 × 5 (exponent form: 3 × 5)

    All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    Prime factor81524Highest power
    223—2323
    3—333
    5—5—5

    LCM = 23 × 3 × 5 = 120

    Checking the LCM of 8, 15 and 24 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, 15) = (8 × 15) ÷ 1 = 120 ÷ 1 = 120

    LCM(120, 24) = (120 × 24) ÷ 24 = 2,880 ÷ 24 = 120

    LCM(8, 15, 24) = 120

    The pairs may be taken in any order — 15 and 24 first, then 8 — and the answer is the same 120. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/8--15--24Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/8--15--24">What is the LCM of 8, 15 and 24? - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    What is the LCM of 8, 15 and 24?. The LCM of 8, 15 and 24 is 120 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/8--15--24/generated.jpgCopy

    LCM Table

    Number 1Number 2Number 3LCM
    8915360
    81015120
    811151,320
    81215120
    813151,560
    81415840
    81515120
    81516240
    815172,040
    81518360
    815192,280
    81520120
    81521840
    815221,320
    815232,760
    81524120
    81525600
    815261,560
    815271,080
    81528840
    815293,480
    81530120
    815313,720
    81532480
    815331,320
    815342,040
    81535840
    81536360
    815374,440
    815382,280

    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, 15 and 24? (The answer is: 120). Enter the first number (e.g. '8'), the second (e.g. '15') and the third (e.g. '24'), 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, 15 and 24?

    LCM of 8, 15 and 24 is 120

    How to find the LCM of 8, 15 and 24 by prime factorization?

    Take every prime that appears in 8, 15 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

    Can you get the LCM of 8, 15 and 24 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 15 is 120, and the LCM of 120 and 24 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, 15 and 24?

    Yes, and by definition it is the smallest positive integer that is: 120 ÷ 8, 120 ÷ 15 and 120 ÷ 24 all come out whole. Any other common multiple of 8, 15 and 24 is a multiple of 120.

    See Also