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    LCM for 12, 16 and 50

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

    What's the Least Common Multiple (LCM) of 12, 16 and 50?

    Answer

    LCM of 12, 16 and 50 is
    1,200

    (One thousand two hundred)

    1,200 is the smallest positive integer that 12, 16 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 12, 16 and 50 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

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

    All Prime Factors of 50: 2 × 5 × 5 (exponent form: 2 × 52)

    Prime factor121650Highest power
    22224224
    33——3
    5——5252

    LCM = 24 × 3 × 52 = 1,200

    Checking the LCM of 12, 16 and 50 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(12, 16) = (12 × 16) ÷ 4 = 192 ÷ 4 = 48

    LCM(48, 50) = (48 × 50) ÷ 2 = 2,400 ÷ 2 = 1,200

    LCM(12, 16, 50) = 1,200

    The pairs may be taken in any order — 16 and 50 first, then 12 — and the answer is the same 1,200. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 12, 16 and 50?. The LCM of 12, 16 and 50 is 1,200 — 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
    1216351,680
    121636144
    1216371,776
    121638912
    121639624
    121640240
    1216411,968
    121642336
    1216432,064
    121644528
    121645720
    1216461,104
    1216472,256
    12164848
    1216492,352
    1216501,200
    121651816
    121652624
    1216532,544
    121654432
    1216552,640
    121656336
    121657912
    1216581,392
    1216592,832
    121660240
    1216612,928
    1216621,488
    1216631,008
    121664192

    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 12, 16 and 50? (The answer is: 1,200). Enter the first number (e.g. '12'), the second (e.g. '16') and the third (e.g. '50'), 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 12, 16 and 50?

    LCM of 12, 16 and 50 is 1,200

    How to find the LCM of 12, 16 and 50 by prime factorization?

    Take every prime that appears in 12, 16 and 50 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 5² = 1,200.

    Can you get the LCM of 12, 16 and 50 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 12 and 16 is 48, and the LCM of 48 and 50 is 1,200 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 1,200 divisible by 12, 16 and 50?

    Yes, and by definition it is the smallest positive integer that is: 1,200 ÷ 12, 1,200 ÷ 16 and 1,200 ÷ 50 all come out whole. Any other common multiple of 12, 16 and 50 is a multiple of 1,200.

    See Also