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    LCM for 30, 40 and 50

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

    What's the Least Common Multiple (LCM) of 30, 40 and 50?

    Answer

    LCM of 30, 40 and 50 is
    600

    (Six hundred)

    600 is the smallest positive integer that 30, 40 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 30, 40 and 50 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

    All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

    All Prime Factors of 50: 2 × 5 × 5 (exponent form: 2 × 52)

    Prime factor304050Highest power
    2223223
    33——3
    5555252

    LCM = 23 × 3 × 52 = 600

    Checking the LCM of 30, 40 and 50 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(30, 40) = (30 × 40) ÷ 10 = 1,200 ÷ 10 = 120

    LCM(120, 50) = (120 × 50) ÷ 10 = 6,000 ÷ 10 = 600

    LCM(30, 40, 50) = 600

    The pairs may be taken in any order — 40 and 50 first, then 30 — and the answer is the same 600. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 30, 40 and 50?. The LCM of 30, 40 and 50 is 600 — 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
    303540840
    303640360
    3037404,440
    3038402,280
    3039401,560
    304040120
    3040414,920
    304042840
    3040435,160
    3040441,320
    304045360
    3040462,760
    3040475,640
    304048240
    3040495,880
    304050600
    3040512,040
    3040521,560
    3040536,360
    3040541,080
    3040551,320
    304056840
    3040572,280
    3040583,480
    3040597,080
    304060120
    3040617,320
    3040623,720
    3040632,520
    304064960

    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 30, 40 and 50? (The answer is: 600). Enter the first number (e.g. '30'), the second (e.g. '40') and the third (e.g. '50'), 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 30, 40 and 50?

    LCM of 30, 40 and 50 is 600

    How to find the LCM of 30, 40 and 50 by prime factorization?

    Take every prime that appears in 30, 40 and 50 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5² = 600.

    Can you get the LCM of 30, 40 and 50 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 30 and 40 is 120, and the LCM of 120 and 50 is 600 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 600 divisible by 30, 40 and 50?

    Yes, and by definition it is the smallest positive integer that is: 600 ÷ 30, 600 ÷ 40 and 600 ÷ 50 all come out whole. Any other common multiple of 30, 40 and 50 is a multiple of 600.

    See Also