Calculators & Converters

    6, 9 and 12 LCM

    LCM - Least Common Multiple Calculator

    LCM of 6, 9 and 12 is equal to 36. The comprehensive work provides more insight of how to find what is the lcm of 6, 9 and 12 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 6, 9 and 12?
    lcm (6   9   12) = (?)
    6 => 2 x 3
    9 => 3 x 3
    12 => 2 x 2 x 3

    = 2 x 3 x 3 x 2
    = 36
    lcm (6, 9 and 12) = 36
    36 is the lcm of 6, 9 and 12.

    where,
    6 is a positive integer,
    9 is a positive integer,
    36 is the lcm of 6, 9 and 12,
    {2, 3} in {2 x 3, 3 x 3, 2 x 2 x 3} are the most repeated factors of 6, 9 and 12,
    {3, 2} in {2 x 3, 3 x 3, 2 x 2 x 3} are the the other remaining factors of 6, 9 and 12.

    Use in Mathematics: LCM of 6, 9 and 12
    The below are some of the mathematical applications where lcm of 6, 9 and 12 can be used:

    1. to find the least number which is exactly divisible by 6, 9 and 12.
    2. to find the common denominators for the fractions having 6, 9 and 12 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 6, 9 and 12 lcm
    In the context of lcm real world problems, the lcm of 6, 9 and 12 helps to find the exact time when three similar and recurring with different time schedule happens together at the same time. For example, the real world problems involve lcm in situations to find at what time all the bells A, B and C toll together, if bell A tolls at 6 seconds, B tolls at 9 seconds and C tolls at 12 seconds repeatedly. The answer is that all bells A, B and C toll together at 36 seconds for the first time, at 72 seconds for the second time, at 108 seconds for the third time and so on.

    Important Notes: 6, 9 and 12 lcm
    The below are the important notes to be remembered while solving the lcm of 6, 9 and 12:
    1. The repeated and non-repeated prime factors of 6, 9 and 12 should be multiplied to find the least common multiple of 6, 9 and 12, when solving lcm by using prime factors method.
    2. The results of lcm of 6, 9 and 12 is identical even if we change the order of given numbers in the lcm calculation, it means the order of given numbers in the lcm calculation doesn't affect the results.
    For values other than 6, 9 and 12, use this below tool:

    How-to: What is the LCM of 6, 9 and 12?

    The below solved example with step by step work shows how to find what is the lcm of 6, 9 and 12 by using either prime factors method and special division method.

    Solved example using prime factors method:
    What is the LCM of 6, 9 and 12?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 6
    B = 9
    C = 12

    What to be found:
    find the lcm of 6, 9 and 12

    step 2 Find the prime factors of 6, 9 and 12:
    Prime factors of 6 = 2 x 3
    Prime factors of 9 = 3 x 3
    Prime factors of 12 = 2 x 2 x 3

    step 3 Identify the repeated and non-repeated prime factors of 6, 9 and 12:
    {2, 3} are the most repeated factors and {3, 2} are the non-repeated factors of 6, 9 and 12.

    step 4 Find the product of repeated and non-repeated prime factors of 6, 9 and 12:
    = 2 x 3 x 3 x 2
    = 36
    lcm(20 and 30) = 36

    Hence,
    lcm of 6, 9 and 12 is 36


    Solved example using special division method:
    This special division method is the easiest way to understand the entire calculation of what is the lcm of 6, 9 and 12.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 6, 9 and 12

    What to be found:
    lcm (6, 9, 12) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    6, 9 and 12

    step 3 Choose the divisor which divides each or most of the given integers (6, 9 and 12), divide each integers separately and write down the quotient in the next line right under the respective integers. Bring down the integer to the next line if any integer in 6, 9 and 12 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    26912
    2396
    3393
    3131
    111

    step 4 Multiply the divisors to find the lcm of 6, 9 and 12:
    = 2 x 2 x 3 x 3
    = 36
    LCM(6, 9, 12) = 36

    The least common multiple for three numbers 6, 9 and 12 is 36
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