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    LCM for 9, 10 and 15

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

    What's the Least Common Multiple (LCM) of 9, 10 and 15?

    Answer

    LCM of 9, 10 and 15 is
    90

    (Ninety)

    90 is the smallest positive integer that 9, 10 and 15 all divide without a remainder — every other common multiple of the three is a multiple of it.

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

    All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

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

    Prime factor91015Highest power
    2—2—2
    332—332
    5—555

    LCM = 2 × 32 × 5 = 90

    Checking the LCM of 9, 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(9, 10) = (9 × 10) ÷ 1 = 90 ÷ 1 = 90

    LCM(90, 15) = (90 × 15) ÷ 15 = 1,350 ÷ 15 = 90

    LCM(9, 10, 15) = 90

    The pairs may be taken in any order — 10 and 15 first, then 9 — and the answer is the same 90. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 9, 10 and 15?. The LCM of 9, 10 and 15 is 90 — 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
    191090
    291090
    391090
    4910180
    591090
    691090
    7910630
    8910360
    991090
    9101090
    91011990
    91012180
    910131,170
    91014630
    9101590
    91016720
    910171,530
    9101890
    910191,710
    91020180
    91021630
    91022990
    910232,070
    91024360
    91025450
    910261,170
    91027270
    910281,260
    910292,610
    9103090

    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, 10 and 15? (The answer is: 90). Enter the first number (e.g. '9'), 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 9, 10 and 15?

    LCM of 9, 10 and 15 is 90

    How to find the LCM of 9, 10 and 15 by prime factorization?

    Take every prime that appears in 9, 10 and 15 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

    Can you get the LCM of 9, 10 and 15 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 9 and 10 is 90, and the LCM of 90 and 15 is 90 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 90 divisible by 9, 10 and 15?

    Yes, and by definition it is the smallest positive integer that is: 90 ÷ 9, 90 ÷ 10 and 90 ÷ 15 all come out whole. Any other common multiple of 9, 10 and 15 is a multiple of 90.

    See Also