Calculators & Converters

    28 and 108 LCM

    LCM - Least Common Multiple Calculator

    LCM of 28 and 108 is equal to 756. The comprehensive work provides more insight of how to find what is the lcm of 28 and 108 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 28 and 108?
    lcm (28   108) = (?)
    28 => 2 x 2 x 7
    108 => 2 x 2 x 3 x 3 x 3

    = 2 x 2 x 7 x 3 x 3 x 3
    = 756
    lcm (28 and 108) = 756
    756 is the lcm of 28 and 108.

    where,
    28 is a positive integer,
    108 is a positive integer,
    756 is the lcm of 28 and 108,
    {2 x 2} in {2 x 2 x 7, 2 x 2 x 3 x 3 x 3} are the common factors of 28 and 108,
    {7 x 3 x 3 x 3} in {2 x 2 x 7, 2 x 2 x 3 x 3 x 3} are the uncommon factors of 28 and 108.

    Use in Mathematics: LCM of 28 and 108
    The below are some of the mathematical applications where lcm of 28 and 108 can be used:

    1. to find the least number which is exactly divisible by 28 and 108.
    2. to find the common denominator for two fractions having 28 and 108 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 28 and 108 lcm
    In the context of lcm real world problems, the lcm of 28 and 108 helps to find the exact time when two similar and recurring events 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 the bells A and B all toll together, if bell A tolls at 28 seconds and bell B tolls at 108 seconds repeatedly. The answer is that all bells A and B toll together at 756 seconds for the first time, at 1512 seconds for the second time, at 2268 seconds for the third time and so on.

    Important Notes: 28 and 108 lcm
    The below are the important notes to be remembered while solving the lcm of 28 and 108:
    1. The common prime factors and the remaining prime factors of 28 and 108 should be multiplied to find the least common multiple of 28 and 108, when solving lcm by using prime factors method.
    2. The results of lcm of 28 and 108, and the lcm of 108 and 28 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
    For values other than 28 and 108, use this below tool:

    How-to: What is the LCM of 28 and 108?

    The below solved example with step by step work shows how to find what is the lcm of 28 and 108 by using prime factors method and division method.

    Solved example using prime factors method:
    What is the LCM of 28 and 108?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 28
    B = 108

    What to be found:
    find the lcm of 28 and 108

    step 2 Find the prime factors of 28 and 108:
    Prime factors of 28 = 2 x 2 x 7
    Prime factors of 108 = 2 x 2 x 3 x 3 x 3

    step 3 Identify the repeated and non-repeated prime factors of 28 and 108:
    {2, 2} are the most repeated factors and {7 x 3 x 3 x 3} are the non-repeated factors of 28 and 108.

    step 4 Find the product of repeated and non-repeated prime factors of 28 and 108:
    = 2 x 2 x 7 x 3 x 3 x 3
    = 756
    lcm(28 and 108) = 756

    Hence,
    lcm of 28 and 108 is 756


    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 28 and 108.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 28 and 108

    What to be found:
    lcm (28, 108) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    28 and 108

    step 3 Choose the divisor which divides each or most of the given integers (28 and 108), 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 28 and 108 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    228108
    21454
    3727
    379
    373
    771
    11

    step 4 Multiply the divisors to find the lcm of 28 and 108:
    = 2 x 2 x 3 x 3 x 3 x 7
    = 756
    LCM(28, 108) = 756

    The least common multiple for two numbers 28 and 108 is 756
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