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    LCM for 25, 30 and 50

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

    What's the Least Common Multiple (LCM) of 25, 30 and 50?

    Answer

    LCM of 25, 30 and 50 is
    150

    (One hundred fifty)

    150 is the smallest positive integer that 25, 30 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 25, 30 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 25: 5 × 5 (exponent form: 52)

    All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

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

    Prime factor253050Highest power
    2—222
    3—3—3
    55255252

    LCM = 2 × 3 × 52 = 150

    Checking the LCM of 25, 30 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(25, 30) = (25 × 30) ÷ 5 = 750 ÷ 5 = 150

    LCM(150, 50) = (150 × 50) ÷ 50 = 7,500 ÷ 50 = 150

    LCM(25, 30, 50) = 150

    The pairs may be taken in any order — 30 and 50 first, then 25 — and the answer is the same 150. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 25, 30 and 50?. The LCM of 25, 30 and 50 is 150 — 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
    2530351,050
    253036900
    2530375,550
    2530382,850
    2530391,950
    253040600
    2530416,150
    2530421,050
    2530436,450
    2530443,300
    253045450
    2530463,450
    2530477,050
    2530481,200
    2530497,350
    253050150
    2530512,550
    2530523,900
    2530537,950
    2530541,350
    2530551,650
    2530564,200
    2530572,850
    2530584,350
    2530598,850
    253060300
    2530619,150
    2530624,650
    2530633,150
    2530644,800

    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 25, 30 and 50? (The answer is: 150). Enter the first number (e.g. '25'), the second (e.g. '30') 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 25, 30 and 50?

    LCM of 25, 30 and 50 is 150

    How to find the LCM of 25, 30 and 50 by prime factorization?

    Take every prime that appears in 25, 30 and 50 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5² = 150.

    Can you get the LCM of 25, 30 and 50 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 25 and 30 is 150, and the LCM of 150 and 50 is 150 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 150 divisible by 25, 30 and 50?

    Yes, and by definition it is the smallest positive integer that is: 150 ÷ 25, 150 ÷ 30 and 150 ÷ 50 all come out whole. Any other common multiple of 25, 30 and 50 is a multiple of 150.

    See Also