Calculators & Converters

    42, 45 and 48 LCM

    LCM - Least Common Multiple Calculator

    LCM of 42, 45 and 48 is equal to 5040. The comprehensive work provides more insight of how to find what is the lcm of 42, 45 and 48 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 42, 45 and 48?
    lcm (42   45   48) = (?)
    42 => 2 x 3 x 7
    45 => 3 x 3 x 5
    48 => 2 x 2 x 2 x 2 x 3

    = 2 x 3 x 7 x 3 x 5 x 2 x 2 x 2
    = 5040
    lcm (42, 45 and 48) = 5040
    5040 is the lcm of 42, 45 and 48.

    where,
    42 is a positive integer,
    45 is a positive integer,
    5040 is the lcm of 42, 45 and 48,
    {2, 3} in {2 x 3 x 7, 3 x 3 x 5, 2 x 2 x 2 x 2 x 3} are the most repeated factors of 42, 45 and 48,
    {7, 3, 5, 2, 2, 2} in {2 x 3 x 7, 3 x 3 x 5, 2 x 2 x 2 x 2 x 3} are the the other remaining factors of 42, 45 and 48.

    Use in Mathematics: LCM of 42, 45 and 48
    The below are some of the mathematical applications where lcm of 42, 45 and 48 can be used:

    1. to find the least number which is exactly divisible by 42, 45 and 48.
    2. to find the common denominators for the fractions having 42, 45 and 48 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 42, 45 and 48 lcm
    In the context of lcm real world problems, the lcm of 42, 45 and 48 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 42 seconds, B tolls at 45 seconds and C tolls at 48 seconds repeatedly. The answer is that all bells A, B and C toll together at 5040 seconds for the first time, at 10080 seconds for the second time, at 15120 seconds for the third time and so on.

    Important Notes: 42, 45 and 48 lcm
    The below are the important notes to be remembered while solving the lcm of 42, 45 and 48:
    1. The repeated and non-repeated prime factors of 42, 45 and 48 should be multiplied to find the least common multiple of 42, 45 and 48, when solving lcm by using prime factors method.
    2. The results of lcm of 42, 45 and 48 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 42, 45 and 48, use this below tool:

    How-to: What is the LCM of 42, 45 and 48?

    The below solved example with step by step work shows how to find what is the lcm of 42, 45 and 48 by using either prime factors method and special division method.

    Solved example using prime factors method:
    What is the LCM of 42, 45 and 48?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 42
    B = 45
    C = 48

    What to be found:
    find the lcm of 42, 45 and 48

    step 2 Find the prime factors of 42, 45 and 48:
    Prime factors of 42 = 2 x 3 x 7
    Prime factors of 45 = 3 x 3 x 5
    Prime factors of 48 = 2 x 2 x 2 x 2 x 3

    step 3 Identify the repeated and non-repeated prime factors of 42, 45 and 48:
    {2, 3} are the most repeated factors and {7, 3, 5, 2, 2, 2} are the non-repeated factors of 42, 45 and 48.

    step 4 Find the product of repeated and non-repeated prime factors of 42, 45 and 48:
    = 2 x 3 x 7 x 3 x 5 x 2 x 2 x 2
    = 5040
    lcm(20 and 30) = 5040

    Hence,
    lcm of 42, 45 and 48 is 5040


    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 42, 45 and 48.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 42, 45 and 48

    What to be found:
    lcm (42, 45, 48) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    42, 45 and 48

    step 3 Choose the divisor which divides each or most of the given integers (42, 45 and 48), 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 42, 45 and 48 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    2424548
    2214524
    2214512
    221456
    321453
    37151
    5751
    7711
    111

    step 4 Multiply the divisors to find the lcm of 42, 45 and 48:
    = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7
    = 5040
    LCM(42, 45, 48) = 5040

    The least common multiple for three numbers 42, 45 and 48 is 5040
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