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    LCM for 20, 28 and 36

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

    What's the Least Common Multiple (LCM) of 20, 28 and 36?

    Answer

    LCM of 20, 28 and 36 is
    1,260

    (One thousand two hundred sixty)

    1,260 is the smallest positive integer that 20, 28 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 20, 28 and 36 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 28: 2 × 2 × 7 (exponent form: 22 × 7)

    All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

    Prime factor202836Highest power
    222222222
    3——3232
    55——5
    7—7—7

    LCM = 22 × 32 × 5 × 7 = 1,260

    Checking the LCM of 20, 28 and 36 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, 28) = (20 × 28) ÷ 4 = 560 ÷ 4 = 140

    LCM(140, 36) = (140 × 36) ÷ 4 = 5,040 ÷ 4 = 1,260

    LCM(20, 28, 36) = 1,260

    The pairs may be taken in any order — 28 and 36 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, 28 and 36?. The LCM of 20, 28 and 36 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
    202128420
    2022281,540
    2023283,220
    202428840
    202528700
    2026281,820
    2027283,780
    202828140
    2028294,060
    202830420
    2028314,340
    2028321,120
    2028334,620
    2028342,380
    202835140
    2028361,260
    2028375,180
    2028382,660
    2028395,460
    202840280
    2028415,740
    202842420
    2028436,020
    2028441,540
    2028451,260
    2028463,220
    2028476,580
    2028481,680
    202849980
    202850700

    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, 28 and 36? (The answer is: 1,260). Enter the first number (e.g. '20'), the second (e.g. '28') and the third (e.g. '36'), 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, 28 and 36?

    LCM of 20, 28 and 36 is 1,260

    How to find the LCM of 20, 28 and 36 by prime factorization?

    Take every prime that appears in 20, 28 and 36 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, 28 and 36 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 20 and 28 is 140, and the LCM of 140 and 36 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, 28 and 36?

    Yes, and by definition it is the smallest positive integer that is: 1,260 ÷ 20, 1,260 ÷ 28 and 1,260 ÷ 36 all come out whole. Any other common multiple of 20, 28 and 36 is a multiple of 1,260.

    See Also