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    LCM for 25, 30 and 40

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

    What's the Least Common Multiple (LCM) of 25, 30 and 40?

    Answer

    LCM of 25, 30 and 40 is
    600

    (Six hundred)

    600 is the smallest positive integer that 25, 30 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 25, 30 and 40 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 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

    Prime factor253040Highest power
    2—22323
    3—3—3
    5525552

    LCM = 23 × 3 × 52 = 600

    Checking the LCM of 25, 30 and 40 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, 40) = (150 × 40) ÷ 10 = 6,000 ÷ 10 = 600

    LCM(25, 30, 40) = 600

    The pairs may be taken in any order — 30 and 40 first, then 25 — and the answer is the same 600. 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 40?. The LCM of 25, 30 and 40 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
    252530150
    2526301,950
    2527301,350
    2528302,100
    2529304,350
    253030150
    2530314,650
    2530322,400
    2530331,650
    2530342,550
    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

    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 40? (The answer is: 600). Enter the first number (e.g. '25'), the second (e.g. '30') and the third (e.g. '40'), 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 40?

    LCM of 25, 30 and 40 is 600

    How to find the LCM of 25, 30 and 40 by prime factorization?

    Take every prime that appears in 25, 30 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5² = 600.

    Can you get the LCM of 25, 30 and 40 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 40 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 25, 30 and 40?

    Yes, and by definition it is the smallest positive integer that is: 600 ÷ 25, 600 ÷ 30 and 600 ÷ 40 all come out whole. Any other common multiple of 25, 30 and 40 is a multiple of 600.

    See Also