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    LCM for 16, 20 and 24

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

    What's the Least Common Multiple (LCM) of 16, 20 and 24?

    Answer

    LCM of 16, 20 and 24 is
    240

    (Two hundred forty)

    240 is the smallest positive integer that 16, 20 and 24 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 16, 20 and 24 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

    All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    Prime factor162024Highest power
    224222324
    3——33
    5—5—5

    LCM = 24 × 3 × 5 = 240

    Checking the LCM of 16, 20 and 24 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, 20) = (16 × 20) ÷ 4 = 320 ÷ 4 = 80

    LCM(80, 24) = (80 × 24) ÷ 8 = 1,920 ÷ 8 = 240

    LCM(16, 20, 24) = 240

    The pairs may be taken in any order — 20 and 24 first, then 16 — 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 16, 20 and 24?. The LCM of 16, 20 and 24 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
    91620720
    10162080
    111620880
    121620240
    1316201,040
    141620560
    151620240
    16162080
    1617201,360
    161820720
    1619201,520
    16202080
    1620211,680
    162022880
    1620231,840
    162024240
    162025400
    1620261,040
    1620272,160
    162028560
    1620292,320
    162030240
    1620312,480
    162032160
    1620332,640
    1620341,360
    162035560
    162036720
    1620372,960
    1620381,520

    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, 20 and 24? (The answer is: 240). Enter the first number (e.g. '16'), the second (e.g. '20') and the third (e.g. '24'), 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, 20 and 24?

    LCM of 16, 20 and 24 is 240

    How to find the LCM of 16, 20 and 24 by prime factorization?

    Take every prime that appears in 16, 20 and 24 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 5 = 240.

    Can you get the LCM of 16, 20 and 24 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 16 and 20 is 80, and the LCM of 80 and 24 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 16, 20 and 24?

    Yes, and by definition it is the smallest positive integer that is: 240 ÷ 16, 240 ÷ 20 and 240 ÷ 24 all come out whole. Any other common multiple of 16, 20 and 24 is a multiple of 240.

    See Also