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    LCM for 60, 75 and 111

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

    What's the Least Common Multiple (LCM) of 60, 75 and 111?

    Answer

    LCM of 60, 75 and 111 is
    11,100

    (Eleven thousand one hundred)

    11,100 is the smallest positive integer that 60, 75 and 111 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 60, 75 and 111 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 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

    All Prime Factors of 75: 3 × 5 × 5 (exponent form: 3 × 52)

    All Prime Factors of 111: 3 × 37 (exponent form: 3 × 37)

    Prime factor6075111Highest power
    222——22
    33333
    5552—52
    37——3737

    LCM = 22 × 3 × 52 × 37 = 11,100

    Checking the LCM of 60, 75 and 111 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(60, 75) = (60 × 75) ÷ 15 = 4,500 ÷ 15 = 300

    LCM(300, 111) = (300 × 111) ÷ 3 = 33,300 ÷ 3 = 11,100

    LCM(60, 75, 111) = 11,100

    The pairs may be taken in any order — 75 and 111 first, then 60 — and the answer is the same 11,100. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 60, 75 and 111?. The LCM of 60, 75 and 111 is 11,100 — 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
    6075962,400
    60759729,100
    60759814,700
    6075999,900
    6075100300
    607510130,300
    60751025,100
    607510330,900
    60751047,800
    60751052,100
    607510615,900
    607510732,100
    60751082,700
    607510932,700
    60751103,300
    607511111,100
    60751128,400
    607511333,900
    60751145,700
    60751156,900
    60751168,700
    607511711,700
    607511817,700
    607511935,700
    6075120600
    607512136,300
    607512218,300
    607512312,300
    60751249,300
    60751251,500

    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 60, 75 and 111? (The answer is: 11,100). Enter the first number (e.g. '60'), the second (e.g. '75') and the third (e.g. '111'), 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 60, 75 and 111?

    LCM of 60, 75 and 111 is 11,100

    How to find the LCM of 60, 75 and 111 by prime factorization?

    Take every prime that appears in 60, 75 and 111 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² × 37 = 11,100.

    Can you get the LCM of 60, 75 and 111 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 60 and 75 is 300, and the LCM of 300 and 111 is 11,100 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 11,100 divisible by 60, 75 and 111?

    Yes, and by definition it is the smallest positive integer that is: 11,100 ÷ 60, 11,100 ÷ 75 and 11,100 ÷ 111 all come out whole. Any other common multiple of 60, 75 and 111 is a multiple of 11,100.

    See Also