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    LCM for 16, 48 and 64

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

    What's the Least Common Multiple (LCM) of 16, 48 and 64?

    Answer

    LCM of 16, 48 and 64 is
    192

    (One hundred ninety-two)

    192 is the smallest positive integer that 16, 48 and 64 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 16, 48 and 64 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 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

    All Prime Factors of 64: 2 × 2 × 2 × 2 × 2 × 2 (exponent form: 26)

    Prime factor164864Highest power
    224242626
    3—3—3

    LCM = 26 × 3 = 192

    Checking the LCM of 16, 48 and 64 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, 48) = (16 × 48) ÷ 16 = 768 ÷ 16 = 48

    LCM(48, 64) = (48 × 64) ÷ 16 = 3,072 ÷ 16 = 192

    LCM(16, 48, 64) = 192

    The pairs may be taken in any order — 48 and 64 first, then 16 — and the answer is the same 192. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 16, 48 and 64?. The LCM of 16, 48 and 64 is 192 — 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
    1648492,352
    1648501,200
    164851816
    164852624
    1648532,544
    164854432
    1648552,640
    164856336
    164857912
    1648581,392
    1648592,832
    164860240
    1648612,928
    1648621,488
    1648631,008
    164864192
    1648653,120
    164866528
    1648673,216
    164868816
    1648691,104
    1648701,680
    1648713,408
    164872144
    1648733,504
    1648741,776
    1648751,200
    164876912
    1648773,696
    164878624

    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, 48 and 64? (The answer is: 192). Enter the first number (e.g. '16'), the second (e.g. '48') and the third (e.g. '64'), 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, 48 and 64?

    LCM of 16, 48 and 64 is 192

    How to find the LCM of 16, 48 and 64 by prime factorization?

    Take every prime that appears in 16, 48 and 64 to the highest power it reaches in any one of them and multiply: 2⁶ × 3 = 192.

    Can you get the LCM of 16, 48 and 64 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 16 and 48 is 48, and the LCM of 48 and 64 is 192 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 192 divisible by 16, 48 and 64?

    Yes, and by definition it is the smallest positive integer that is: 192 ÷ 16, 192 ÷ 48 and 192 ÷ 64 all come out whole. Any other common multiple of 16, 48 and 64 is a multiple of 192.

    See Also