Calculators & Converters

    48, 60 and 64 LCM

    LCM - Least Common Multiple Calculator

    LCM of 48, 60 and 64 is equal to 960. The comprehensive work provides more insight of how to find what is the lcm of 48, 60 and 64 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 48, 60 and 64?
    lcm (48   60   64) = (?)
    48 => 2 x 2 x 2 x 2 x 3
    60 => 2 x 2 x 3 x 5
    64 => 2 x 2 x 2 x 2 x 2 x 2

    = 2 x 2 x 2 x 2 x 3 x 5 x 2 x 2
    = 960
    lcm (48, 60 and 64) = 960
    960 is the lcm of 48, 60 and 64.

    where,
    48 is a positive integer,
    60 is a positive integer,
    960 is the lcm of 48, 60 and 64,
    {2, 2, 2, 2, 3} in {2 x 2 x 2 x 2 x 3, 2 x 2 x 3 x 5, 2 x 2 x 2 x 2 x 2 x 2} are the most repeated factors of 48, 60 and 64,
    {5, 2, 2} in {2 x 2 x 2 x 2 x 3, 2 x 2 x 3 x 5, 2 x 2 x 2 x 2 x 2 x 2} are the the other remaining factors of 48, 60 and 64.

    Use in Mathematics: LCM of 48, 60 and 64
    The below are some of the mathematical applications where lcm of 48, 60 and 64 can be used:

    1. to find the least number which is exactly divisible by 48, 60 and 64.
    2. to find the common denominators for the fractions having 48, 60 and 64 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 48, 60 and 64 lcm
    In the context of lcm real world problems, the lcm of 48, 60 and 64 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 48 seconds, B tolls at 60 seconds and C tolls at 64 seconds repeatedly. The answer is that all bells A, B and C toll together at 960 seconds for the first time, at 1920 seconds for the second time, at 2880 seconds for the third time and so on.

    Important Notes: 48, 60 and 64 lcm
    The below are the important notes to be remembered while solving the lcm of 48, 60 and 64:
    1. The repeated and non-repeated prime factors of 48, 60 and 64 should be multiplied to find the least common multiple of 48, 60 and 64, when solving lcm by using prime factors method.
    2. The results of lcm of 48, 60 and 64 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 48, 60 and 64, use this below tool:

    How-to: What is the LCM of 48, 60 and 64?

    The below solved example with step by step work shows how to find what is the lcm of 48, 60 and 64 by using either prime factors method and special division method.

    Solved example using prime factors method:
    What is the LCM of 48, 60 and 64?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 48
    B = 60
    C = 64

    What to be found:
    find the lcm of 48, 60 and 64

    step 2 Find the prime factors of 48, 60 and 64:
    Prime factors of 48 = 2 x 2 x 2 x 2 x 3
    Prime factors of 60 = 2 x 2 x 3 x 5
    Prime factors of 64 = 2 x 2 x 2 x 2 x 2 x 2

    step 3 Identify the repeated and non-repeated prime factors of 48, 60 and 64:
    {2, 2, 2, 2, 3} are the most repeated factors and {5, 2, 2} are the non-repeated factors of 48, 60 and 64.

    step 4 Find the product of repeated and non-repeated prime factors of 48, 60 and 64:
    = 2 x 2 x 2 x 2 x 3 x 5 x 2 x 2
    = 960
    lcm(20 and 30) = 960

    Hence,
    lcm of 48, 60 and 64 is 960


    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 48, 60 and 64.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 48, 60 and 64

    What to be found:
    lcm (48, 60, 64) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    48, 60 and 64

    step 3 Choose the divisor which divides each or most of the given integers (48, 60 and 64), 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 48, 60 and 64 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    2486064
    2243032
    2121516
    26158
    23154
    23152
    33151
    5151
    111

    step 4 Multiply the divisors to find the lcm of 48, 60 and 64:
    = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5
    = 960
    LCM(48, 60, 64) = 960

    The least common multiple for three numbers 48, 60 and 64 is 960
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