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    LCM for 25, 50 and 100

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

    What's the Least Common Multiple (LCM) of 25, 50 and 100?

    Answer

    LCM of 25, 50 and 100 is
    100

    (One hundred)

    100 is the smallest positive integer that 25, 50 and 100 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 25, 50 and 100 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 50: 2 × 5 × 5 (exponent form: 2 × 52)

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

    Prime factor2550100Highest power
    2—22222
    552525252

    LCM = 22 × 52 = 100

    Checking the LCM of 25, 50 and 100 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, 50) = (25 × 50) ÷ 25 = 1,250 ÷ 25 = 50

    LCM(50, 100) = (50 × 100) ÷ 50 = 5,000 ÷ 50 = 100

    LCM(25, 50, 100) = 100

    The pairs may be taken in any order — 50 and 100 first, then 25 — and the answer is the same 100. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 25, 50 and 100?. The LCM of 25, 50 and 100 is 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
    255085850
    2550862,150
    2550874,350
    2550882,200
    2550894,450
    255090450
    2550914,550
    2550922,300
    2550934,650
    2550942,350
    255095950
    2550962,400
    2550974,850
    2550982,450
    2550994,950
    2550100100
    25501015,050
    25501022,550
    25501035,150
    25501042,600
    25501051,050
    25501062,650
    25501075,350
    25501082,700
    25501095,450
    2550110550
    25501115,550
    25501122,800
    25501135,650
    25501142,850

    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, 50 and 100? (The answer is: 100). Enter the first number (e.g. '25'), the second (e.g. '50') and the third (e.g. '100'), 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, 50 and 100?

    LCM of 25, 50 and 100 is 100

    How to find the LCM of 25, 50 and 100 by prime factorization?

    Take every prime that appears in 25, 50 and 100 to the highest power it reaches in any one of them and multiply: 2² × 5² = 100.

    Can you get the LCM of 25, 50 and 100 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 25 and 50 is 50, and the LCM of 50 and 100 is 100 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 100 divisible by 25, 50 and 100?

    Yes, and by definition it is the smallest positive integer that is: 100 ÷ 25, 100 ÷ 50 and 100 ÷ 100 all come out whole. Any other common multiple of 25, 50 and 100 is a multiple of 100.

    See Also