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    LCM for 15, 175 and 225

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

    What's the Least Common Multiple (LCM) of 15, 175 and 225?

    Answer

    LCM of 15, 175 and 225 is
    1,575

    (One thousand five hundred seventy-five)

    1,575 is the smallest positive integer that 15, 175 and 225 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 15, 175 and 225 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 175: 5 × 5 × 7 (exponent form: 52 × 7)

    All Prime Factors of 225: 3 × 3 × 5 × 5 (exponent form: 32 × 52)

    Prime factor15175225Highest power
    33—3232
    55525252
    7—7—7

    LCM = 32 × 52 × 7 = 1,575

    Checking the LCM of 15, 175 and 225 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, 175) = (15 × 175) ÷ 5 = 2,625 ÷ 5 = 525

    LCM(525, 225) = (525 × 225) ÷ 75 = 118,125 ÷ 75 = 1,575

    LCM(15, 175, 225) = 1,575

    The pairs may be taken in any order — 175 and 225 first, then 15 — and the answer is the same 1,575. That is exactly why the two routes on this page agree.

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    What is the LCM of 15, 175 and 225?. The LCM of 15, 175 and 225 is 1,575 — 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
    151752101,050
    15175211110,775
    15175212111,300
    1517521337,275
    15175214112,350
    1517521522,575
    1517521637,800
    1517521716,275
    15175218114,450
    1517521938,325
    1517522023,100
    15175221116,025
    1517522238,850
    15175223117,075
    1517522416,800
    151752251,575
    15175226118,650
    15175227119,175
    1517522839,900
    15175229120,225
    1517523024,150
    151752315,775
    15175232121,800
    15175233122,325
    1517523440,950
    1517523524,675
    15175236123,900
    1517523741,475
    1517523817,850
    15175239125,475

    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, 175 and 225? (The answer is: 1,575). Enter the first number (e.g. '15'), the second (e.g. '175') and the third (e.g. '225'), 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, 175 and 225?

    LCM of 15, 175 and 225 is 1,575

    How to find the LCM of 15, 175 and 225 by prime factorization?

    Take every prime that appears in 15, 175 and 225 to the highest power it reaches in any one of them and multiply: 3² × 5² × 7 = 1,575.

    Can you get the LCM of 15, 175 and 225 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 15 and 175 is 525, and the LCM of 525 and 225 is 1,575 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 1,575 divisible by 15, 175 and 225?

    Yes, and by definition it is the smallest positive integer that is: 1,575 ÷ 15, 1,575 ÷ 175 and 1,575 ÷ 225 all come out whole. Any other common multiple of 15, 175 and 225 is a multiple of 1,575.

    See Also