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    LCM for 10, 20 and 35

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

    What's the Least Common Multiple (LCM) of 10, 20 and 35?

    Answer

    LCM of 10, 20 and 35 is
    140

    (One hundred forty)

    140 is the smallest positive integer that 10, 20 and 35 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 10, 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 10: 2 × 5 (exponent form: 2 × 5)

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

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

    Prime factor102035Highest power
    2222—22
    55555
    7——77

    LCM = 22 × 5 × 7 = 140

    Checking the LCM of 10, 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(10, 20) = (10 × 20) ÷ 10 = 200 ÷ 10 = 20

    LCM(20, 35) = (20 × 35) ÷ 5 = 700 ÷ 5 = 140

    LCM(10, 20, 35) = 140

    The pairs may be taken in any order — 20 and 35 first, then 10 — 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 10, 20 and 35?. The LCM of 10, 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
    10202020
    102021420
    102022220
    102023460
    102024120
    102025100
    102026260
    102027540
    102028140
    102029580
    10203060
    102031620
    102032160
    102033660
    102034340
    102035140
    102036180
    102037740
    102038380
    102039780
    10204040
    102041820
    102042420
    102043860
    102044220
    102045180
    102046460
    102047940
    102048240
    102049980

    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 10, 20 and 35? (The answer is: 140). Enter the first number (e.g. '10'), 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 10, 20 and 35?

    LCM of 10, 20 and 35 is 140

    How to find the LCM of 10, 20 and 35 by prime factorization?

    Take every prime that appears in 10, 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 10, 20 and 35 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 10 and 20 is 20, and the LCM of 20 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 10, 20 and 35?

    Yes, and by definition it is the smallest positive integer that is: 140 ÷ 10, 140 ÷ 20 and 140 ÷ 35 all come out whole. Any other common multiple of 10, 20 and 35 is a multiple of 140.

    See Also