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    LCM for 10, 14 and 15

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

    What's the Least Common Multiple (LCM) of 10, 14 and 15?

    Answer

    LCM of 10, 14 and 15 is
    210

    (Two hundred ten)

    210 is the smallest positive integer that 10, 14 and 15 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 10, 14 and 15 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 14: 2 × 7 (exponent form: 2 × 7)

    All Prime Factors of 15: 3 × 5 (exponent form: 3 × 5)

    Prime factor101415Highest power
    222—2
    3——33
    55—55
    7—7—7

    LCM = 2 × 3 × 5 × 7 = 210

    Checking the LCM of 10, 14 and 15 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, 14) = (10 × 14) ÷ 2 = 140 ÷ 2 = 70

    LCM(70, 15) = (70 × 15) ÷ 5 = 1,050 ÷ 5 = 210

    LCM(10, 14, 15) = 210

    The pairs may be taken in any order — 14 and 15 first, then 10 — and the answer is the same 210. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 10, 14 and 15?. The LCM of 10, 14 and 15 is 210 — 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
    1101470
    2101470
    31014210
    41014140
    5101470
    61014210
    7101470
    81014280
    91014630
    10101470
    101114770
    101214420
    101314910
    10141470
    101415210
    101416560
    1014171,190
    101418630
    1014191,330
    101420140
    101421210
    101422770
    1014231,610
    101424840
    101425350
    101426910
    1014271,890
    101428140
    1014292,030
    101430210

    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, 14 and 15? (The answer is: 210). Enter the first number (e.g. '10'), the second (e.g. '14') and the third (e.g. '15'), 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, 14 and 15?

    LCM of 10, 14 and 15 is 210

    How to find the LCM of 10, 14 and 15 by prime factorization?

    Take every prime that appears in 10, 14 and 15 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5 × 7 = 210.

    Can you get the LCM of 10, 14 and 15 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 10 and 14 is 70, and the LCM of 70 and 15 is 210 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 210 divisible by 10, 14 and 15?

    Yes, and by definition it is the smallest positive integer that is: 210 ÷ 10, 210 ÷ 14 and 210 ÷ 15 all come out whole. Any other common multiple of 10, 14 and 15 is a multiple of 210.

    See Also