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    LCM for 20, 35 and 45

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

    What's the Least Common Multiple (LCM) of 20, 35 and 45?

    Answer

    LCM of 20, 35 and 45 is
    1,260

    (One thousand two hundred sixty)

    1,260 is the smallest positive integer that 20, 35 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 20, 35 and 45 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

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

    All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

    Prime factor203545Highest power
    222——22
    3——3232
    55555
    7—7—7

    LCM = 22 × 32 × 5 × 7 = 1,260

    Checking the LCM of 20, 35 and 45 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(20, 35) = (20 × 35) ÷ 5 = 700 ÷ 5 = 140

    LCM(140, 45) = (140 × 45) ÷ 5 = 6,300 ÷ 5 = 1,260

    LCM(20, 35, 45) = 1,260

    The pairs may be taken in any order — 35 and 45 first, then 20 — and the answer is the same 1,260. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 20, 35 and 45?. The LCM of 20, 35 and 45 is 1,260 — 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
    203035420
    2031354,340
    2032351,120
    2033354,620
    2034352,380
    203535140
    2035361,260
    2035375,180
    2035382,660
    2035395,460
    203540280
    2035415,740
    203542420
    2035436,020
    2035441,540
    2035451,260
    2035463,220
    2035476,580
    2035481,680
    203549980
    203550700
    2035517,140
    2035521,820
    2035537,420
    2035543,780
    2035551,540
    203556280
    2035577,980
    2035584,060
    2035598,260

    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 20, 35 and 45? (The answer is: 1,260). Enter the first number (e.g. '20'), the second (e.g. '35') and the third (e.g. '45'), 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 20, 35 and 45?

    LCM of 20, 35 and 45 is 1,260

    How to find the LCM of 20, 35 and 45 by prime factorization?

    Take every prime that appears in 20, 35 and 45 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 × 7 = 1,260.

    Can you get the LCM of 20, 35 and 45 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 20 and 35 is 140, and the LCM of 140 and 45 is 1,260 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 1,260 divisible by 20, 35 and 45?

    Yes, and by definition it is the smallest positive integer that is: 1,260 ÷ 20, 1,260 ÷ 35 and 1,260 ÷ 45 all come out whole. Any other common multiple of 20, 35 and 45 is a multiple of 1,260.

    See Also