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    LCM for 7, 12 and 16

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

    What's the Least Common Multiple (LCM) of 7, 12 and 16?

    Answer

    LCM of 7, 12 and 16 is
    336

    (Three hundred thirty-six)

    336 is the smallest positive integer that 7, 12 and 16 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 7, 12 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 7: 7 (exponent form: 7)

    All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

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

    Prime factor71216Highest power
    2—222424
    3—3—3
    77——7

    LCM = 24 × 3 × 7 = 336

    Checking the LCM of 7, 12 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(7, 12) = (7 × 12) ÷ 1 = 84 ÷ 1 = 84

    LCM(84, 16) = (84 × 16) ÷ 4 = 1,344 ÷ 4 = 336

    LCM(7, 12, 16) = 336

    The pairs may be taken in any order — 12 and 16 first, then 7 — and the answer is the same 336. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 7, 12 and 16?. The LCM of 7, 12 and 16 is 336 — 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
    171284
    271284
    371284
    471284
    5712420
    671284
    771284
    7812168
    7912252
    71012420
    71112924
    7121284
    712131,092
    7121484
    71215420
    71216336
    712171,428
    71218252
    712191,596
    71220420
    7122184
    71222924
    712231,932
    71224168
    712252,100
    712261,092
    71227756
    7122884
    712292,436
    71230420

    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 7, 12 and 16? (The answer is: 336). Enter the first number (e.g. '7'), the second (e.g. '12') 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 7, 12 and 16?

    LCM of 7, 12 and 16 is 336

    How to find the LCM of 7, 12 and 16 by prime factorization?

    Take every prime that appears in 7, 12 and 16 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 7 = 336.

    Can you get the LCM of 7, 12 and 16 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 7 and 12 is 84, and the LCM of 84 and 16 is 336 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 336 divisible by 7, 12 and 16?

    Yes, and by definition it is the smallest positive integer that is: 336 ÷ 7, 336 ÷ 12 and 336 ÷ 16 all come out whole. Any other common multiple of 7, 12 and 16 is a multiple of 336.

    See Also