Calculators & Converters

    45 and 75 LCM

    LCM - Least Common Multiple Calculator

    LCM of 45 and 75 is equal to 225. The comprehensive work provides more insight of how to find what is the lcm of 45 and 75 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 and 75?
    lcm (45   75) = (?)
    45 => 3 x 3 x 5
    75 => 3 x 5 x 5

    = 3 x 5 x 3 x 5
    = 225
    lcm (45 and 75) = 225
    225 is the lcm of 45 and 75.

    where,
    45 is a positive integer,
    75 is a positive integer,
    225 is the lcm of 45 and 75,
    {3 x 5} in {3 x 3 x 5, 3 x 5 x 5} are the common factors of 45 and 75,
    {3 x 5} in {3 x 3 x 5, 3 x 5 x 5} are the uncommon factors of 45 and 75.

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

    1. to find the least number which is exactly divisible by 45 and 75.
    2. to find the common denominator for two fractions having 45 and 75 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 45 and 75 lcm
    In the context of lcm real world problems, the lcm of 45 and 75 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 45 seconds and bell B tolls at 75 seconds repeatedly. The answer is that all bells A and B toll together at 225 seconds for the first time, at 450 seconds for the second time, at 675 seconds for the third time and so on.

    Important Notes: 45 and 75 lcm
    The below are the important notes to be remembered while solving the lcm of 45 and 75:
    1. The common prime factors and the remaining prime factors of 45 and 75 should be multiplied to find the least common multiple of 45 and 75, when solving lcm by using prime factors method.
    2. The results of lcm of 45 and 75, and the lcm of 75 and 45 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
    For values other than 45 and 75, use this below tool:

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

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

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

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

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

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

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

    step 4 Find the product of repeated and non-repeated prime factors of 45 and 75:
    = 3 x 5 x 3 x 5
    = 225
    lcm(45 and 75) = 225

    Hence,
    lcm of 45 and 75 is 225


    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 and 75.

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

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

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

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

    34575
    31525
    5525
    515
    11

    step 4 Multiply the divisors to find the lcm of 45 and 75:
    = 3 x 3 x 5 x 5
    = 225
    LCM(45, 75) = 225

    The least common multiple for two numbers 45 and 75 is 225
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