Calculators & Converters

    15, 24 and 27 LCM

    LCM - Least Common Multiple Calculator

    LCM of 15, 24 and 27 is equal to 1080. The comprehensive work provides more insight of how to find what is the lcm of 15, 24 and 27 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 15, 24 and 27?
    lcm (15   24   27) = (?)
    15 => 3 x 5
    24 => 2 x 2 x 2 x 3
    27 => 3 x 3 x 3

    = 3 x 5 x 2 x 2 x 2 x 3 x 3
    = 1080
    lcm (15, 24 and 27) = 1080
    1080 is the lcm of 15, 24 and 27.

    where,
    15 is a positive integer,
    24 is a positive integer,
    1080 is the lcm of 15, 24 and 27,
    {3} in {3 x 5, 2 x 2 x 2 x 3, 3 x 3 x 3} is the most repeated factors of 15, 24 and 27,
    {5, 2, 2, 2, 3, 3} in {3 x 5, 2 x 2 x 2 x 3, 3 x 3 x 3} are the the other remaining factors of 15, 24 and 27.

    Use in Mathematics: LCM of 15, 24 and 27
    The below are some of the mathematical applications where lcm of 15, 24 and 27 can be used:

    1. to find the least number which is exactly divisible by 15, 24 and 27.
    2. to find the common denominators for the fractions having 15, 24 and 27 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 15, 24 and 27 lcm
    In the context of lcm real world problems, the lcm of 15, 24 and 27 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 15 seconds, B tolls at 24 seconds and C tolls at 27 seconds repeatedly. The answer is that all bells A, B and C toll together at 1080 seconds for the first time, at 2160 seconds for the second time, at 3240 seconds for the third time and so on.

    Important Notes: 15, 24 and 27 lcm
    The below are the important notes to be remembered while solving the lcm of 15, 24 and 27:
    1. The repeated and non-repeated prime factors of 15, 24 and 27 should be multiplied to find the least common multiple of 15, 24 and 27, when solving lcm by using prime factors method.
    2. The results of lcm of 15, 24 and 27 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 15, 24 and 27, use this below tool:

    How-to: What is the LCM of 15, 24 and 27?

    The below solved example with step by step work shows how to find what is the lcm of 15, 24 and 27 by using either prime factors method and special division method.

    Solved example using prime factors method:
    What is the LCM of 15, 24 and 27?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 15
    B = 24
    C = 27

    What to be found:
    find the lcm of 15, 24 and 27

    step 2 Find the prime factors of 15, 24 and 27:
    Prime factors of 15 = 3 x 5
    Prime factors of 24 = 2 x 2 x 2 x 3
    Prime factors of 27 = 3 x 3 x 3

    step 3 Identify the repeated and non-repeated prime factors of 15, 24 and 27:
    {3} is the most repeated factor and {5, 2, 2, 2, 3, 3} are the non-repeated factors of 15, 24 and 27.

    step 4 Find the product of repeated and non-repeated prime factors of 15, 24 and 27:
    = 3 x 5 x 2 x 2 x 2 x 3 x 3
    = 1080
    lcm(20 and 30) = 1080

    Hence,
    lcm of 15, 24 and 27 is 1080


    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 15, 24 and 27.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 15, 24 and 27

    What to be found:
    lcm (15, 24, 27) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    15, 24 and 27

    step 3 Choose the divisor which divides each or most of the given integers (15, 24 and 27), 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 15, 24 and 27 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    2152427
    2151227
    215627
    315327
    3519
    3513
    5511
    111

    step 4 Multiply the divisors to find the lcm of 15, 24 and 27:
    = 2 x 2 x 2 x 3 x 3 x 3 x 5
    = 1080
    LCM(15, 24, 27) = 1080

    The least common multiple for three numbers 15, 24 and 27 is 1080
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