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    LCM for 50, 100 and 150

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

    What's the Least Common Multiple (LCM) of 50, 100 and 150?

    Answer

    LCM of 50, 100 and 150 is
    300

    (Three hundred)

    300 is the smallest positive integer that 50, 100 and 150 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 50, 100 and 150 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 50: 2 × 5 × 5 (exponent form: 2 × 52)

    All Prime Factors of 100: 2 × 2 × 5 × 5 (exponent form: 22 × 52)

    All Prime Factors of 150: 2 × 3 × 5 × 5 (exponent form: 2 × 3 × 52)

    Prime factor50100150Highest power
    2222222
    3——33
    552525252

    LCM = 22 × 3 × 52 = 300

    Checking the LCM of 50, 100 and 150 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(50, 100) = (50 × 100) ÷ 50 = 5,000 ÷ 50 = 100

    LCM(100, 150) = (100 × 150) ÷ 50 = 15,000 ÷ 50 = 300

    LCM(50, 100, 150) = 300

    The pairs may be taken in any order — 100 and 150 first, then 50 — and the answer is the same 300. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 50, 100 and 150?. The LCM of 50, 100 and 150 is 300 — 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
    501001352,700
    501001363,400
    5010013713,700
    501001386,900
    5010013913,900
    50100140700
    5010014114,100
    501001427,100
    5010014314,300
    501001443,600
    501001452,900
    501001467,300
    5010014714,700
    501001483,700
    5010014914,900
    50100150300
    5010015115,100
    501001523,800
    5010015315,300
    501001547,700
    501001553,100
    501001563,900
    5010015715,700
    501001587,900
    5010015915,900
    50100160800
    5010016116,100
    501001628,100
    5010016316,300
    501001644,100

    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 50, 100 and 150? (The answer is: 300). Enter the first number (e.g. '50'), the second (e.g. '100') and the third (e.g. '150'), 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 50, 100 and 150?

    LCM of 50, 100 and 150 is 300

    How to find the LCM of 50, 100 and 150 by prime factorization?

    Take every prime that appears in 50, 100 and 150 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

    Can you get the LCM of 50, 100 and 150 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 50 and 100 is 100, and the LCM of 100 and 150 is 300 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 300 divisible by 50, 100 and 150?

    Yes, and by definition it is the smallest positive integer that is: 300 ÷ 50, 300 ÷ 100 and 300 ÷ 150 all come out whole. Any other common multiple of 50, 100 and 150 is a multiple of 300.

    See Also