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    LCM for 4, 15 and 16

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

    What's the Least Common Multiple (LCM) of 4, 15 and 16?

    Answer

    LCM of 4, 15 and 16 is
    240

    (Two hundred forty)

    240 is the smallest positive integer that 4, 15 and 16 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 4, 15 and 16 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 15: 3 × 5 (exponent form: 3 × 5)

    All Prime Factors of 16: 2 × 2 × 2 × 2 (exponent form: 24)

    Prime factor41516Highest power
    222—2424
    3—3—3
    5—5—5

    LCM = 24 × 3 × 5 = 240

    Checking the LCM of 4, 15 and 16 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, 15) = (4 × 15) ÷ 1 = 60 ÷ 1 = 60

    LCM(60, 16) = (60 × 16) ÷ 4 = 960 ÷ 4 = 240

    LCM(4, 15, 16) = 240

    The pairs may be taken in any order — 15 and 16 first, then 4 — and the answer is the same 240. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 4, 15 and 16?. The LCM of 4, 15 and 16 is 240 — 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
    141560
    241560
    341560
    441560
    451560
    461560
    4715420
    4815120
    4915180
    4101560
    41115660
    4121560
    41315780
    41415420
    4151560
    41516240
    415171,020
    41518180
    415191,140
    4152060
    41521420
    41522660
    415231,380
    41524120
    41525300
    41526780
    41527540
    41528420
    415291,740
    4153060

    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, 15 and 16? (The answer is: 240). Enter the first number (e.g. '4'), the second (e.g. '15') and the third (e.g. '16'), 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, 15 and 16?

    LCM of 4, 15 and 16 is 240

    How to find the LCM of 4, 15 and 16 by prime factorization?

    Take every prime that appears in 4, 15 and 16 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 5 = 240.

    Can you get the LCM of 4, 15 and 16 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 4 and 15 is 60, and the LCM of 60 and 16 is 240 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 240 divisible by 4, 15 and 16?

    Yes, and by definition it is the smallest positive integer that is: 240 ÷ 4, 240 ÷ 15 and 240 ÷ 16 all come out whole. Any other common multiple of 4, 15 and 16 is a multiple of 240.

    See Also