Calculators & Converters

    84 and 144 LCM

    LCM - Least Common Multiple Calculator

    LCM of 84 and 144 is equal to 1008. The comprehensive work provides more insight of how to find what is the lcm of 84 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 84 and 144?
    lcm (84   144) = (?)
    84 => 2 x 2 x 3 x 7
    144 => 2 x 2 x 2 x 2 x 3 x 3

    = 2 x 2 x 3 x 7 x 2 x 2 x 3
    = 1008
    lcm (84 and 144) = 1008
    1008 is the lcm of 84 and 144.

    where,
    84 is a positive integer,
    144 is a positive integer,
    1008 is the lcm of 84 and 144,
    {2 x 2 x 3} in {2 x 2 x 3 x 7, 2 x 2 x 2 x 2 x 3 x 3} are the common factors of 84 and 144,
    {7 x 2 x 2 x 3} in {2 x 2 x 3 x 7, 2 x 2 x 2 x 2 x 3 x 3} are the uncommon factors of 84 and 144.

    Use in Mathematics: LCM of 84 and 144
    The below are some of the mathematical applications where lcm of 84 and 144 can be used:

    1. to find the least number which is exactly divisible by 84 and 144.
    2. to find the common denominator for two fractions having 84 and 144 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 84 and 144 lcm
    In the context of lcm real world problems, the lcm of 84 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 84 seconds and bell B tolls at 144 seconds repeatedly. The answer is that all bells A and B toll together at 1008 seconds for the first time, at 2016 seconds for the second time, at 3024 seconds for the third time and so on.

    Important Notes: 84 and 144 lcm
    The below are the important notes to be remembered while solving the lcm of 84 and 144:
    1. The common prime factors and the remaining prime factors of 84 and 144 should be multiplied to find the least common multiple of 84 and 144, when solving lcm by using prime factors method.
    2. The results of lcm of 84 and 144, and the lcm of 144 and 84 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
    For values other than 84 and 144, use this below tool:

    How-to: What is the LCM of 84 and 144?

    The below solved example with step by step work shows how to find what is the lcm of 84 and 144 by using prime factors method and division method.

    Solved example using prime factors method:
    What is the LCM of 84 and 144?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 84
    B = 144

    What to be found:
    find the lcm of 84 and 144

    step 2 Find the prime factors of 84 and 144:
    Prime factors of 84 = 2 x 2 x 3 x 7
    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 84 and 144:
    {2, 2, 3} are the most repeated factors and {7 x 2 x 2 x 3} are the non-repeated factors of 84 and 144.

    step 4 Find the product of repeated and non-repeated prime factors of 84 and 144:
    = 2 x 2 x 3 x 7 x 2 x 2 x 3
    = 1008
    lcm(84 and 144) = 1008

    Hence,
    lcm of 84 and 144 is 1008


    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 84 and 144.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 84 and 144

    What to be found:
    lcm (84, 144) = ?

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

    step 3 Choose the divisor which divides each or most of the given integers (84 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 84 and 144 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    284144
    24272
    22136
    22118
    3219
    373
    771
    11

    step 4 Multiply the divisors to find the lcm of 84 and 144:
    = 2 x 2 x 2 x 2 x 3 x 3 x 7
    = 1008
    LCM(84, 144) = 1008

    The least common multiple for two numbers 84 and 144 is 1008
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