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    LCM for 7, 14 and 16

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

    What's the Least Common Multiple (LCM) of 7, 14 and 16?

    Answer

    LCM of 7, 14 and 16 is
    112

    (One hundred twelve)

    112 is the smallest positive integer that 7, 14 and 16 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 7, 14 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 14: 2 × 7 (exponent form: 2 × 7)

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

    Prime factor71416Highest power
    2—22424
    777—7

    LCM = 24 × 7 = 112

    Checking the LCM of 7, 14 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, 14) = (7 × 14) ÷ 7 = 98 ÷ 7 = 14

    LCM(14, 16) = (14 × 16) ÷ 2 = 224 ÷ 2 = 112

    LCM(7, 14, 16) = 112

    The pairs may be taken in any order — 14 and 16 first, then 7 — and the answer is the same 112. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 7, 14 and 16?. The LCM of 7, 14 and 16 is 112 — 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
    171414
    271414
    371442
    471428
    571470
    671442
    771414
    781456
    7914126
    7101470
    71114154
    7121484
    71314182
    7141414
    71415210
    71416112
    71417238
    71418126
    71419266
    71420140
    7142142
    71422154
    71423322
    71424168
    71425350
    71426182
    71427378
    7142828
    71429406
    71430210

    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, 14 and 16? (The answer is: 112). Enter the first number (e.g. '7'), the second (e.g. '14') 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, 14 and 16?

    LCM of 7, 14 and 16 is 112

    How to find the LCM of 7, 14 and 16 by prime factorization?

    Take every prime that appears in 7, 14 and 16 to the highest power it reaches in any one of them and multiply: 2⁴ × 7 = 112.

    Can you get the LCM of 7, 14 and 16 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 7 and 14 is 14, and the LCM of 14 and 16 is 112 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 112 divisible by 7, 14 and 16?

    Yes, and by definition it is the smallest positive integer that is: 112 ÷ 7, 112 ÷ 14 and 112 ÷ 16 all come out whole. Any other common multiple of 7, 14 and 16 is a multiple of 112.

    See Also