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    LCM for 156, 195 and 390

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

    What's the Least Common Multiple (LCM) of 156, 195 and 390?

    Answer

    LCM of 156, 195 and 390 is
    780

    (Seven hundred eighty)

    780 is the smallest positive integer that 156, 195 and 390 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 156, 195 and 390 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 156: 2 × 2 × 3 × 13 (exponent form: 22 × 3 × 13)

    All Prime Factors of 195: 3 × 5 × 13 (exponent form: 3 × 5 × 13)

    All Prime Factors of 390: 2 × 3 × 5 × 13 (exponent form: 2 × 3 × 5 × 13)

    Prime factor156195390Highest power
    222—222
    33333
    5—555
    1313131313

    LCM = 22 × 3 × 5 × 13 = 780

    Checking the LCM of 156, 195 and 390 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(156, 195) = (156 × 195) ÷ 39 = 30,420 ÷ 39 = 780

    LCM(780, 390) = (780 × 390) ÷ 390 = 304,200 ÷ 390 = 780

    LCM(156, 195, 390) = 780

    The pairs may be taken in any order — 195 and 390 first, then 156 — and the answer is the same 780. That is exactly why the two routes on this page agree.

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    What is the LCM of 156, 195 and 390?. The LCM of 156, 195 and 390 is 780 — 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
    15619537519,500
    15619537673,320
    15619537722,620
    15619537849,140
    156195379295,620
    15619538014,820
    15619538199,060
    156195382148,980
    156195383298,740
    15619538424,960
    15619538560,060
    156195386150,540
    156195387100,620
    15619538875,660
    156195389303,420
    156195390780
    156195391304,980
    15619539276,440
    156195393102,180
    156195394153,660
    15619539561,620
    15619539625,740
    156195397309,660
    156195398155,220
    156195399103,740
    15619540015,600
    156195401312,780
    15619540252,260
    15619540324,180
    15619540478,780

    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 156, 195 and 390? (The answer is: 780). Enter the first number (e.g. '156'), the second (e.g. '195') and the third (e.g. '390'), 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 156, 195 and 390?

    LCM of 156, 195 and 390 is 780

    How to find the LCM of 156, 195 and 390 by prime factorization?

    Take every prime that appears in 156, 195 and 390 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 13 = 780.

    Can you get the LCM of 156, 195 and 390 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 156 and 195 is 780, and the LCM of 780 and 390 is 780 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 780 divisible by 156, 195 and 390?

    Yes, and by definition it is the smallest positive integer that is: 780 ÷ 156, 780 ÷ 195 and 780 ÷ 390 all come out whole. Any other common multiple of 156, 195 and 390 is a multiple of 780.

    See Also