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    LCM for 4, 9 and 10

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

    What's the Least Common Multiple (LCM) of 4, 9 and 10?

    Answer

    LCM of 4, 9 and 10 is
    180

    (One hundred eighty)

    180 is the smallest positive integer that 4, 9 and 10 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 4, 9 and 10 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 4: 2 × 2 (exponent form: 22)

    All Prime Factors of 9: 3 × 3 (exponent form: 32)

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

    Prime factor4910Highest power
    222—222
    3—32—32
    5——55

    LCM = 22 × 32 × 5 = 180

    Checking the LCM of 4, 9 and 10 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(4, 9) = (4 × 9) ÷ 1 = 36 ÷ 1 = 36

    LCM(36, 10) = (36 × 10) ÷ 2 = 360 ÷ 2 = 180

    LCM(4, 9, 10) = 180

    The pairs may be taken in any order — 9 and 10 first, then 4 — and the answer is the same 180. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 4, 9 and 10?. The LCM of 4, 9 and 10 is 180 — 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
    14936
    24936
    34936
    44936
    459180
    46936
    479252
    48972
    49936
    4910180
    4911396
    491236
    4913468
    4914252
    4915180
    4916144
    4917612
    491836
    4919684
    4920180
    4921252
    4922396
    4923828
    492472
    4925900
    4926468
    4927108
    4928252
    49291,044
    4930180

    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 4, 9 and 10? (The answer is: 180). Enter the first number (e.g. '4'), the second (e.g. '9') and the third (e.g. '10'), 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 4, 9 and 10?

    LCM of 4, 9 and 10 is 180

    How to find the LCM of 4, 9 and 10 by prime factorization?

    Take every prime that appears in 4, 9 and 10 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

    Can you get the LCM of 4, 9 and 10 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 4 and 9 is 36, and the LCM of 36 and 10 is 180 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 180 divisible by 4, 9 and 10?

    Yes, and by definition it is the smallest positive integer that is: 180 ÷ 4, 180 ÷ 9 and 180 ÷ 10 all come out whole. Any other common multiple of 4, 9 and 10 is a multiple of 180.

    See Also