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    LCM for 15, 20 and 25

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

    What's the Least Common Multiple (LCM) of 15, 20 and 25?

    Answer

    LCM of 15, 20 and 25 is
    300

    (Three hundred)

    300 is the smallest positive integer that 15, 20 and 25 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 15, 20 and 25 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

    All Prime Factors of 25: 5 × 5 (exponent form: 52)

    Prime factor152025Highest power
    2—22—22
    33——3
    5555252

    LCM = 22 × 3 × 52 = 300

    Checking the LCM of 15, 20 and 25 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, 20) = (15 × 20) ÷ 5 = 300 ÷ 5 = 60

    LCM(60, 25) = (60 × 25) ÷ 5 = 1,500 ÷ 5 = 300

    LCM(15, 20, 25) = 300

    The pairs may be taken in any order — 20 and 25 first, then 15 — and the answer is the same 300. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 15, 20 and 25?. The LCM of 15, 20 and 25 is 300 — 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
    10152060
    111520660
    12152060
    131520780
    141520420
    15152060
    151620240
    1517201,020
    151820180
    1519201,140
    15202060
    152021420
    152022660
    1520231,380
    152024120
    152025300
    152026780
    152027540
    152028420
    1520291,740
    15203060
    1520311,860
    152032480
    152033660
    1520341,020
    152035420
    152036180
    1520372,220
    1520381,140
    152039780

    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, 20 and 25? (The answer is: 300). Enter the first number (e.g. '15'), the second (e.g. '20') and the third (e.g. '25'), 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, 20 and 25?

    LCM of 15, 20 and 25 is 300

    How to find the LCM of 15, 20 and 25 by prime factorization?

    Take every prime that appears in 15, 20 and 25 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

    Can you get the LCM of 15, 20 and 25 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 15 and 20 is 60, and the LCM of 60 and 25 is 300 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 300 divisible by 15, 20 and 25?

    Yes, and by definition it is the smallest positive integer that is: 300 ÷ 15, 300 ÷ 20 and 300 ÷ 25 all come out whole. Any other common multiple of 15, 20 and 25 is a multiple of 300.

    See Also