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    LCM for 7, 20 and 35

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

    What's the Least Common Multiple (LCM) of 7, 20 and 35?

    Answer

    LCM of 7, 20 and 35 is
    140

    (One hundred forty)

    140 is the smallest positive integer that 7, 20 and 35 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 7, 20 and 35 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 7: 7 (exponent form: 7)

    All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

    All Prime Factors of 35: 5 × 7 (exponent form: 5 × 7)

    Prime factor72035Highest power
    2—22—22
    5—555
    77—77

    LCM = 22 × 5 × 7 = 140

    Checking the LCM of 7, 20 and 35 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(7, 20) = (7 × 20) ÷ 1 = 140 ÷ 1 = 140

    LCM(140, 35) = (140 × 35) ÷ 35 = 4,900 ÷ 35 = 140

    LCM(7, 20, 35) = 140

    The pairs may be taken in any order — 20 and 35 first, then 7 — and the answer is the same 140. That is exactly why the two routes on this page agree.

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    What is the LCM of 7, 20 and 35?. The LCM of 7, 20 and 35 is 140 — 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
    72020140
    72021420
    720221,540
    720233,220
    72024840
    72025700
    720261,820
    720273,780
    72028140
    720294,060
    72030420
    720314,340
    720321,120
    720334,620
    720342,380
    72035140
    720361,260
    720375,180
    720382,660
    720395,460
    72040280
    720415,740
    72042420
    720436,020
    720441,540
    720451,260
    720463,220
    720476,580
    720481,680
    72049980

    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 7, 20 and 35? (The answer is: 140). Enter the first number (e.g. '7'), the second (e.g. '20') and the third (e.g. '35'), 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 7, 20 and 35?

    LCM of 7, 20 and 35 is 140

    How to find the LCM of 7, 20 and 35 by prime factorization?

    Take every prime that appears in 7, 20 and 35 to the highest power it reaches in any one of them and multiply: 2² × 5 × 7 = 140.

    Can you get the LCM of 7, 20 and 35 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 7 and 20 is 140, and the LCM of 140 and 35 is 140 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 140 divisible by 7, 20 and 35?

    Yes, and by definition it is the smallest positive integer that is: 140 ÷ 7, 140 ÷ 20 and 140 ÷ 35 all come out whole. Any other common multiple of 7, 20 and 35 is a multiple of 140.

    See Also