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    LCM for 16, 36 and 48

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

    What's the Least Common Multiple (LCM) of 16, 36 and 48?

    Answer

    LCM of 16, 36 and 48 is
    144

    (One hundred forty-four)

    144 is the smallest positive integer that 16, 36 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 16, 36 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 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

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

    Prime factor163648Highest power
    224222424
    3—32332

    LCM = 24 × 32 = 144

    Checking the LCM of 16, 36 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, 36) = (16 × 36) ÷ 4 = 576 ÷ 4 = 144

    LCM(144, 48) = (144 × 48) ÷ 48 = 6,912 ÷ 48 = 144

    LCM(16, 36, 48) = 144

    The pairs may be taken in any order — 36 and 48 first, then 16 — and the answer is the same 144. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 16, 36 and 48?. The LCM of 16, 36 and 48 is 144 — 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
    1633361,584
    1634362,448
    1635365,040
    163636144
    1636375,328
    1636382,736
    1636391,872
    163640720
    1636415,904
    1636421,008
    1636436,192
    1636441,584
    163645720
    1636463,312
    1636476,768
    163648144
    1636497,056
    1636503,600
    1636512,448
    1636521,872
    1636537,632
    163654432
    1636557,920
    1636561,008
    1636572,736
    1636584,176
    1636598,496
    163660720
    1636618,784
    1636624,464

    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, 36 and 48? (The answer is: 144). Enter the first number (e.g. '16'), the second (e.g. '36') 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, 36 and 48?

    LCM of 16, 36 and 48 is 144

    How to find the LCM of 16, 36 and 48 by prime factorization?

    Take every prime that appears in 16, 36 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

    Can you get the LCM of 16, 36 and 48 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 16 and 36 is 144, and the LCM of 144 and 48 is 144 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 144 divisible by 16, 36 and 48?

    Yes, and by definition it is the smallest positive integer that is: 144 ÷ 16, 144 ÷ 36 and 144 ÷ 48 all come out whole. Any other common multiple of 16, 36 and 48 is a multiple of 144.

    See Also