Calculators & Converters

    21, 24 and 28 LCM

    LCM - Least Common Multiple Calculator

    LCM of 21, 24 and 28 is equal to 168. The comprehensive work provides more insight of how to find what is the lcm of 21, 24 and 28 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 21, 24 and 28?
    lcm (21   24   28) = (?)
    21 => 3 x 7
    24 => 2 x 2 x 2 x 3
    28 => 2 x 2 x 7

    = 2 x 2 x 3 x 7 x 2
    = 168
    lcm (21, 24 and 28) = 168
    168 is the lcm of 21, 24 and 28.

    where,
    21 is a positive integer,
    24 is a positive integer,
    168 is the lcm of 21, 24 and 28,
    {2, 2, 3, 7} in {3 x 7, 2 x 2 x 2 x 3, 2 x 2 x 7} are the most repeated factors of 21, 24 and 28,
    {2} in {3 x 7, 2 x 2 x 2 x 3, 2 x 2 x 7} is the other remaining factors of 21, 24 and 28.

    Use in Mathematics: LCM of 21, 24 and 28
    The below are some of the mathematical applications where lcm of 21, 24 and 28 can be used:

    1. to find the least number which is exactly divisible by 21, 24 and 28.
    2. to find the common denominators for the fractions having 21, 24 and 28 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 21, 24 and 28 lcm
    In the context of lcm real world problems, the lcm of 21, 24 and 28 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 21 seconds, B tolls at 24 seconds and C tolls at 28 seconds repeatedly. The answer is that all bells A, B and C toll together at 168 seconds for the first time, at 336 seconds for the second time, at 504 seconds for the third time and so on.

    Important Notes: 21, 24 and 28 lcm
    The below are the important notes to be remembered while solving the lcm of 21, 24 and 28:
    1. The repeated and non-repeated prime factors of 21, 24 and 28 should be multiplied to find the least common multiple of 21, 24 and 28, when solving lcm by using prime factors method.
    2. The results of lcm of 21, 24 and 28 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 21, 24 and 28, use this below tool:

    How-to: What is the LCM of 21, 24 and 28?

    The below solved example with step by step work shows how to find what is the lcm of 21, 24 and 28 by using either prime factors method and special division method.

    Solved example using prime factors method:
    What is the LCM of 21, 24 and 28?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 21
    B = 24
    C = 28

    What to be found:
    find the lcm of 21, 24 and 28

    step 2 Find the prime factors of 21, 24 and 28:
    Prime factors of 21 = 3 x 7
    Prime factors of 24 = 2 x 2 x 2 x 3
    Prime factors of 28 = 2 x 2 x 7

    step 3 Identify the repeated and non-repeated prime factors of 21, 24 and 28:
    {2, 2, 3, 7} are the most repeated factors and {2} is the non-repeated factors of 21, 24 and 28.

    step 4 Find the product of repeated and non-repeated prime factors of 21, 24 and 28:
    = 2 x 2 x 3 x 7 x 2
    = 168
    lcm(20 and 30) = 168

    Hence,
    lcm of 21, 24 and 28 is 168


    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 21, 24 and 28.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 21, 24 and 28

    What to be found:
    lcm (21, 24, 28) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    21, 24 and 28

    step 3 Choose the divisor which divides each or most of the given integers (21, 24 and 28), 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 21, 24 and 28 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    2212428
    2211214
    22167
    32137
    7717
    111

    step 4 Multiply the divisors to find the lcm of 21, 24 and 28:
    = 2 x 2 x 2 x 3 x 7
    = 168
    LCM(21, 24, 28) = 168

    The least common multiple for three numbers 21, 24 and 28 is 168
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