Calculators & Converters

    30, 45 and 84 LCM

    LCM - Least Common Multiple Calculator

    LCM of 30, 45 and 84 is equal to 1260. The comprehensive work provides more insight of how to find what is the lcm of 30, 45 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 30, 45 and 84?
    lcm (30   45   84) = (?)
    30 => 2 x 3 x 5
    45 => 3 x 3 x 5
    84 => 2 x 2 x 3 x 7

    = 2 x 3 x 5 x 3 x 2 x 7
    = 1260
    lcm (30, 45 and 84) = 1260
    1260 is the lcm of 30, 45 and 84.

    where,
    30 is a positive integer,
    45 is a positive integer,
    1260 is the lcm of 30, 45 and 84,
    {2, 3, 5} in {2 x 3 x 5, 3 x 3 x 5, 2 x 2 x 3 x 7} are the most repeated factors of 30, 45 and 84,
    {3, 2, 7} in {2 x 3 x 5, 3 x 3 x 5, 2 x 2 x 3 x 7} are the the other remaining factors of 30, 45 and 84.

    Use in Mathematics: LCM of 30, 45 and 84
    The below are some of the mathematical applications where lcm of 30, 45 and 84 can be used:

    1. to find the least number which is exactly divisible by 30, 45 and 84.
    2. to find the common denominators for the fractions having 30, 45 and 84 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 30, 45 and 84 lcm
    In the context of lcm real world problems, the lcm of 30, 45 and 84 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 30 seconds, B tolls at 45 seconds and C tolls at 84 seconds repeatedly. The answer is that all bells A, B and C toll together at 1260 seconds for the first time, at 2520 seconds for the second time, at 3780 seconds for the third time and so on.

    Important Notes: 30, 45 and 84 lcm
    The below are the important notes to be remembered while solving the lcm of 30, 45 and 84:
    1. The repeated and non-repeated prime factors of 30, 45 and 84 should be multiplied to find the least common multiple of 30, 45 and 84, when solving lcm by using prime factors method.
    2. The results of lcm of 30, 45 and 84 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 30, 45 and 84, use this below tool:

    How-to: What is the LCM of 30, 45 and 84?

    The below solved example with step by step work shows how to find what is the lcm of 30, 45 and 84 by using either prime factors method and special division method.

    Solved example using prime factors method:
    What is the LCM of 30, 45 and 84?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 30
    B = 45
    C = 84

    What to be found:
    find the lcm of 30, 45 and 84

    step 2 Find the prime factors of 30, 45 and 84:
    Prime factors of 30 = 2 x 3 x 5
    Prime factors of 45 = 3 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 30, 45 and 84:
    {2, 3, 5} are the most repeated factors and {3, 2, 7} are the non-repeated factors of 30, 45 and 84.

    step 4 Find the product of repeated and non-repeated prime factors of 30, 45 and 84:
    = 2 x 3 x 5 x 3 x 2 x 7
    = 1260
    lcm(20 and 30) = 1260

    Hence,
    lcm of 30, 45 and 84 is 1260


    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 30, 45 and 84.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 30, 45 and 84

    What to be found:
    lcm (30, 45, 84) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    30, 45 and 84

    step 3 Choose the divisor which divides each or most of the given integers (30, 45 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 30, 45 and 84 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    2304584
    2154542
    3154521
    35157
    5557
    7117
    111

    step 4 Multiply the divisors to find the lcm of 30, 45 and 84:
    = 2 x 2 x 3 x 3 x 5 x 7
    = 1260
    LCM(30, 45, 84) = 1260

    The least common multiple for three numbers 30, 45 and 84 is 1260
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