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    LCM for 16, 32 and 48

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

    What's the Least Common Multiple (LCM) of 16, 32 and 48?

    Answer

    LCM of 16, 32 and 48 is
    96

    (Ninety-six)

    96 is the smallest positive integer that 16, 32 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 16, 32 and 48 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 32: 2 × 2 × 2 × 2 × 2 (exponent form: 25)

    All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

    Prime factor163248Highest power
    224252425
    3——33

    LCM = 25 × 3 = 96

    Checking the LCM of 16, 32 and 48 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, 32) = (16 × 32) ÷ 16 = 512 ÷ 16 = 32

    LCM(32, 48) = (32 × 48) ÷ 16 = 1,536 ÷ 16 = 96

    LCM(16, 32, 48) = 96

    The pairs may be taken in any order — 32 and 48 first, then 16 — and the answer is the same 96. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 16, 32 and 48?. The LCM of 16, 32 and 48 is 96 — 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
    1632331,056
    163234544
    1632351,120
    163236288
    1632371,184
    163238608
    1632391,248
    163240160
    1632411,312
    163242672
    1632431,376
    163244352
    1632451,440
    163246736
    1632471,504
    16324896
    1632491,568
    163250800
    1632511,632
    163252416
    1632531,696
    163254864
    1632551,760
    163256224
    1632571,824
    163258928
    1632591,888
    163260480
    1632611,952
    163262992

    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, 32 and 48? (The answer is: 96). Enter the first number (e.g. '16'), the second (e.g. '32') and the third (e.g. '48'), 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, 32 and 48?

    LCM of 16, 32 and 48 is 96

    How to find the LCM of 16, 32 and 48 by prime factorization?

    Take every prime that appears in 16, 32 and 48 to the highest power it reaches in any one of them and multiply: 2⁵ × 3 = 96.

    Can you get the LCM of 16, 32 and 48 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 16 and 32 is 32, and the LCM of 32 and 48 is 96 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 96 divisible by 16, 32 and 48?

    Yes, and by definition it is the smallest positive integer that is: 96 ÷ 16, 96 ÷ 32 and 96 ÷ 48 all come out whole. Any other common multiple of 16, 32 and 48 is a multiple of 96.

    See Also