Calculators & Converters

    60 and 84 LCM

    LCM - Least Common Multiple Calculator

    LCM of 60 and 84 is equal to 420. The comprehensive work provides more insight of how to find what is the lcm of 60 and 84 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 60 and 84?
    lcm (60   84) = (?)
    60 => 2 x 2 x 3 x 5
    84 => 2 x 2 x 3 x 7

    = 2 x 2 x 3 x 5 x 7
    = 420
    lcm (60 and 84) = 420
    420 is the lcm of 60 and 84.

    where,
    60 is a positive integer,
    84 is a positive integer,
    420 is the lcm of 60 and 84,
    {2 x 2 x 3} in {2 x 2 x 3 x 5, 2 x 2 x 3 x 7} are the common factors of 60 and 84,
    {5 x 7} in {2 x 2 x 3 x 5, 2 x 2 x 3 x 7} are the uncommon factors of 60 and 84.

    Use in Mathematics: LCM of 60 and 84
    The below are some of the mathematical applications where lcm of 60 and 84 can be used:

    1. to find the least number which is exactly divisible by 60 and 84.
    2. to find the common denominator for two fractions having 60 and 84 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 60 and 84 lcm
    In the context of lcm real world problems, the lcm of 60 and 84 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 60 seconds and bell B tolls at 84 seconds repeatedly. The answer is that all bells A and B toll together at 420 seconds for the first time, at 840 seconds for the second time, at 1260 seconds for the third time and so on.

    Important Notes: 60 and 84 lcm
    The below are the important notes to be remembered while solving the lcm of 60 and 84:
    1. The common prime factors and the remaining prime factors of 60 and 84 should be multiplied to find the least common multiple of 60 and 84, when solving lcm by using prime factors method.
    2. The results of lcm of 60 and 84, and the lcm of 84 and 60 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
    For values other than 60 and 84, use this below tool:

    How-to: What is the LCM of 60 and 84?

    The below solved example with step by step work shows how to find what is the lcm of 60 and 84 by using prime factors method and division method.

    Solved example using prime factors method:
    What is the LCM of 60 and 84?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 60
    B = 84

    What to be found:
    find the lcm of 60 and 84

    step 2 Find the prime factors of 60 and 84:
    Prime factors of 60 = 2 x 2 x 3 x 5
    Prime factors of 84 = 2 x 2 x 3 x 7

    step 3 Identify the repeated and non-repeated prime factors of 60 and 84:
    {2, 2, 3} are the most repeated factors and {5 x 7} are the non-repeated factors of 60 and 84.

    step 4 Find the product of repeated and non-repeated prime factors of 60 and 84:
    = 2 x 2 x 3 x 5 x 7
    = 420
    lcm(60 and 84) = 420

    Hence,
    lcm of 60 and 84 is 420


    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 60 and 84.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 60 and 84

    What to be found:
    lcm (60, 84) = ?

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

    step 3 Choose the divisor which divides each or most of the given integers (60 and 84), 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 60 and 84 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    26084
    23042
    31521
    557
    717
    11

    step 4 Multiply the divisors to find the lcm of 60 and 84:
    = 2 x 2 x 3 x 5 x 7
    = 420
    LCM(60, 84) = 420

    The least common multiple for two numbers 60 and 84 is 420
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