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    LCM for 15, 25 and 100

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

    What's the Least Common Multiple (LCM) of 15, 25 and 100?

    Answer

    LCM of 15, 25 and 100 is
    300

    (Three hundred)

    300 is the smallest positive integer that 15, 25 and 100 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 15, 25 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 15: 3 × 5 (exponent form: 3 × 5)

    All Prime Factors of 25: 5 × 5 (exponent form: 52)

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

    Prime factor1525100Highest power
    2——2222
    33——3
    55525252

    LCM = 22 × 3 × 52 = 300

    Checking the LCM of 15, 25 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(15, 25) = (15 × 25) ÷ 5 = 375 ÷ 5 = 75

    LCM(75, 100) = (75 × 100) ÷ 25 = 7,500 ÷ 25 = 300

    LCM(15, 25, 100) = 300

    The pairs may be taken in any order — 25 and 100 first, then 15 — and the answer is the same 300. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 15, 25 and 100?. The LCM of 15, 25 and 100 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
    1525851,275
    1525866,450
    1525872,175
    1525886,600
    1525896,675
    152590450
    1525916,825
    1525926,900
    1525932,325
    1525947,050
    1525951,425
    1525962,400
    1525977,275
    1525987,350
    1525992,475
    1525100300
    15251017,575
    15251022,550
    15251037,725
    15251047,800
    1525105525
    15251067,950
    15251078,025
    15251082,700
    15251098,175
    15251101,650
    15251112,775
    15251128,400
    15251138,475
    15251142,850

    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 15, 25 and 100? (The answer is: 300). Enter the first number (e.g. '15'), the second (e.g. '25') 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 15, 25 and 100?

    LCM of 15, 25 and 100 is 300

    How to find the LCM of 15, 25 and 100 by prime factorization?

    Take every prime that appears in 15, 25 and 100 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

    Can you get the LCM of 15, 25 and 100 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 15 and 25 is 75, and the LCM of 75 and 100 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 15, 25 and 100?

    Yes, and by definition it is the smallest positive integer that is: 300 ÷ 15, 300 ÷ 25 and 300 ÷ 100 all come out whole. Any other common multiple of 15, 25 and 100 is a multiple of 300.

    See Also