Calculators & Converters

    108 and 144 LCM

    LCM - Least Common Multiple Calculator

    LCM of 108 and 144 is equal to 432. The comprehensive work provides more insight of how to find what is the lcm of 108 and 144 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 108 and 144?
    lcm (108   144) = (?)
    108 => 2 x 2 x 3 x 3 x 3
    144 => 2 x 2 x 2 x 2 x 3 x 3

    = 2 x 2 x 3 x 3 x 3 x 2 x 2
    = 432
    lcm (108 and 144) = 432
    432 is the lcm of 108 and 144.

    where,
    108 is a positive integer,
    144 is a positive integer,
    432 is the lcm of 108 and 144,
    {2 x 2 x 3 x 3} in {2 x 2 x 3 x 3 x 3, 2 x 2 x 2 x 2 x 3 x 3} are the common factors of 108 and 144,
    {3 x 2 x 2} in {2 x 2 x 3 x 3 x 3, 2 x 2 x 2 x 2 x 3 x 3} are the uncommon factors of 108 and 144.

    Use in Mathematics: LCM of 108 and 144
    The below are some of the mathematical applications where lcm of 108 and 144 can be used:

    1. to find the least number which is exactly divisible by 108 and 144.
    2. to find the common denominator for two fractions having 108 and 144 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 108 and 144 lcm
    In the context of lcm real world problems, the lcm of 108 and 144 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 108 seconds and bell B tolls at 144 seconds repeatedly. The answer is that all bells A and B toll together at 432 seconds for the first time, at 864 seconds for the second time, at 1296 seconds for the third time and so on.

    Important Notes: 108 and 144 lcm
    The below are the important notes to be remembered while solving the lcm of 108 and 144:
    1. The common prime factors and the remaining prime factors of 108 and 144 should be multiplied to find the least common multiple of 108 and 144, when solving lcm by using prime factors method.
    2. The results of lcm of 108 and 144, and the lcm of 144 and 108 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
    For values other than 108 and 144, use this below tool:

    How-to: What is the LCM of 108 and 144?

    The below solved example with step by step work shows how to find what is the lcm of 108 and 144 by using prime factors method and division method.

    Solved example using prime factors method:
    What is the LCM of 108 and 144?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 108
    B = 144

    What to be found:
    find the lcm of 108 and 144

    step 2 Find the prime factors of 108 and 144:
    Prime factors of 108 = 2 x 2 x 3 x 3 x 3
    Prime factors of 144 = 2 x 2 x 2 x 2 x 3 x 3

    step 3 Identify the repeated and non-repeated prime factors of 108 and 144:
    {2, 2, 3, 3} are the most repeated factors and {3 x 2 x 2} are the non-repeated factors of 108 and 144.

    step 4 Find the product of repeated and non-repeated prime factors of 108 and 144:
    = 2 x 2 x 3 x 3 x 3 x 2 x 2
    = 432
    lcm(108 and 144) = 432

    Hence,
    lcm of 108 and 144 is 432


    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 108 and 144.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 108 and 144

    What to be found:
    lcm (108, 144) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    108 and 144

    step 3 Choose the divisor which divides each or most of the given integers (108 and 144), 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 108 and 144 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    2108144
    25472
    22736
    22718
    3279
    393
    331
    11

    step 4 Multiply the divisors to find the lcm of 108 and 144:
    = 2 x 2 x 2 x 2 x 3 x 3 x 3
    = 432
    LCM(108, 144) = 432

    The least common multiple for two numbers 108 and 144 is 432
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