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    LCM for 9, 15 and 25

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

    What's the Least Common Multiple (LCM) of 9, 15 and 25?

    Answer

    LCM of 9, 15 and 25 is
    225

    (Two hundred twenty-five)

    225 is the smallest positive integer that 9, 15 and 25 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 9, 15 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 9: 3 × 3 (exponent form: 32)

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

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

    Prime factor91525Highest power
    3323—32
    5—55252

    LCM = 32 × 52 = 225

    Checking the LCM of 9, 15 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(9, 15) = (9 × 15) ÷ 3 = 135 ÷ 3 = 45

    LCM(45, 25) = (45 × 25) ÷ 5 = 1,125 ÷ 5 = 225

    LCM(9, 15, 25) = 225

    The pairs may be taken in any order — 15 and 25 first, then 9 — and the answer is the same 225. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 9, 15 and 25?. The LCM of 9, 15 and 25 is 225 — 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
    9101590
    91115495
    91215180
    91315585
    91415630
    9151545
    91516720
    91517765
    9151890
    91519855
    91520180
    91521315
    91522990
    915231,035
    91524360
    91525225
    915261,170
    91527135
    915281,260
    915291,305
    9153090
    915311,395
    915321,440
    91533495
    915341,530
    91535315
    91536180
    915371,665
    915381,710
    91539585

    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 9, 15 and 25? (The answer is: 225). Enter the first number (e.g. '9'), the second (e.g. '15') 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 9, 15 and 25?

    LCM of 9, 15 and 25 is 225

    How to find the LCM of 9, 15 and 25 by prime factorization?

    Take every prime that appears in 9, 15 and 25 to the highest power it reaches in any one of them and multiply: 3² × 5² = 225.

    Can you get the LCM of 9, 15 and 25 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 9 and 15 is 45, and the LCM of 45 and 25 is 225 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 225 divisible by 9, 15 and 25?

    Yes, and by definition it is the smallest positive integer that is: 225 ÷ 9, 225 ÷ 15 and 225 ÷ 25 all come out whole. Any other common multiple of 9, 15 and 25 is a multiple of 225.

    See Also