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    LCM for 16, 28 and 40

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

    What's the Least Common Multiple (LCM) of 16, 28 and 40?

    Answer

    LCM of 16, 28 and 40 is
    560

    (Five hundred sixty)

    560 is the smallest positive integer that 16, 28 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 16, 28 and 40 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

    All Prime Factors of 28: 2 × 2 × 7 (exponent form: 22 × 7)

    All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

    Prime factor162840Highest power
    224222324
    5——55
    7—7—7

    LCM = 24 × 5 × 7 = 560

    Checking the LCM of 16, 28 and 40 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(16, 28) = (16 × 28) ÷ 4 = 448 ÷ 4 = 112

    LCM(112, 40) = (112 × 40) ÷ 8 = 4,480 ÷ 8 = 560

    LCM(16, 28, 40) = 560

    The pairs may be taken in any order — 28 and 40 first, then 16 — and the answer is the same 560. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 16, 28 and 40?. The LCM of 16, 28 and 40 is 560 — 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
    1625282,800
    1626281,456
    1627283,024
    162828112
    1628293,248
    1628301,680
    1628313,472
    162832224
    1628333,696
    1628341,904
    162835560
    1628361,008
    1628374,144
    1628382,128
    1628394,368
    162840560
    1628414,592
    162842336
    1628434,816
    1628441,232
    1628455,040
    1628462,576
    1628475,264
    162848336
    162849784
    1628502,800
    1628515,712
    1628521,456
    1628535,936
    1628543,024

    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 16, 28 and 40? (The answer is: 560). Enter the first number (e.g. '16'), the second (e.g. '28') and the third (e.g. '40'), 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 16, 28 and 40?

    LCM of 16, 28 and 40 is 560

    How to find the LCM of 16, 28 and 40 by prime factorization?

    Take every prime that appears in 16, 28 and 40 to the highest power it reaches in any one of them and multiply: 2⁴ × 5 × 7 = 560.

    Can you get the LCM of 16, 28 and 40 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 16 and 28 is 112, and the LCM of 112 and 40 is 560 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 560 divisible by 16, 28 and 40?

    Yes, and by definition it is the smallest positive integer that is: 560 ÷ 16, 560 ÷ 28 and 560 ÷ 40 all come out whole. Any other common multiple of 16, 28 and 40 is a multiple of 560.

    See Also