Calculators & Converters

    45, 75 and 81 LCM

    LCM - Least Common Multiple Calculator

    LCM of 45, 75 and 81 is equal to 2025. The comprehensive work provides more insight of how to find what is the lcm of 45, 75 and 81 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 45, 75 and 81?
    lcm (45   75   81) = (?)
    45 => 3 x 3 x 5
    75 => 3 x 5 x 5
    81 => 3 x 3 x 3 x 3

    = 3 x 3 x 5 x 5 x 3 x 3
    = 2025
    lcm (45, 75 and 81) = 2025
    2025 is the lcm of 45, 75 and 81.

    where,
    45 is a positive integer,
    75 is a positive integer,
    2025 is the lcm of 45, 75 and 81,
    {3, 3, 5} in {3 x 3 x 5, 3 x 5 x 5, 3 x 3 x 3 x 3} are the most repeated factors of 45, 75 and 81,
    {5, 3, 3} in {3 x 3 x 5, 3 x 5 x 5, 3 x 3 x 3 x 3} are the the other remaining factors of 45, 75 and 81.

    Use in Mathematics: LCM of 45, 75 and 81
    The below are some of the mathematical applications where lcm of 45, 75 and 81 can be used:

    1. to find the least number which is exactly divisible by 45, 75 and 81.
    2. to find the common denominators for the fractions having 45, 75 and 81 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 45, 75 and 81 lcm
    In the context of lcm real world problems, the lcm of 45, 75 and 81 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 45 seconds, B tolls at 75 seconds and C tolls at 81 seconds repeatedly. The answer is that all bells A, B and C toll together at 2025 seconds for the first time, at 4050 seconds for the second time, at 6075 seconds for the third time and so on.

    Important Notes: 45, 75 and 81 lcm
    The below are the important notes to be remembered while solving the lcm of 45, 75 and 81:
    1. The repeated and non-repeated prime factors of 45, 75 and 81 should be multiplied to find the least common multiple of 45, 75 and 81, when solving lcm by using prime factors method.
    2. The results of lcm of 45, 75 and 81 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 45, 75 and 81, use this below tool:

    How-to: What is the LCM of 45, 75 and 81?

    The below solved example with step by step work shows how to find what is the lcm of 45, 75 and 81 by using either prime factors method and special division method.

    Solved example using prime factors method:
    What is the LCM of 45, 75 and 81?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 45
    B = 75
    C = 81

    What to be found:
    find the lcm of 45, 75 and 81

    step 2 Find the prime factors of 45, 75 and 81:
    Prime factors of 45 = 3 x 3 x 5
    Prime factors of 75 = 3 x 5 x 5
    Prime factors of 81 = 3 x 3 x 3 x 3

    step 3 Identify the repeated and non-repeated prime factors of 45, 75 and 81:
    {3, 3, 5} are the most repeated factors and {5, 3, 3} are the non-repeated factors of 45, 75 and 81.

    step 4 Find the product of repeated and non-repeated prime factors of 45, 75 and 81:
    = 3 x 3 x 5 x 5 x 3 x 3
    = 2025
    lcm(20 and 30) = 2025

    Hence,
    lcm of 45, 75 and 81 is 2025


    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 45, 75 and 81.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 45, 75 and 81

    What to be found:
    lcm (45, 75, 81) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    45, 75 and 81

    step 3 Choose the divisor which divides each or most of the given integers (45, 75 and 81), 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 45, 75 and 81 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    3457581
    3152527
    35259
    35253
    55251
    5151
    111

    step 4 Multiply the divisors to find the lcm of 45, 75 and 81:
    = 3 x 3 x 3 x 3 x 5 x 5
    = 2025
    LCM(45, 75, 81) = 2025

    The least common multiple for three numbers 45, 75 and 81 is 2025
    getcalc.com Calculators