Calculators & Converters

    21, 35 and 45 LCM

    LCM - Least Common Multiple Calculator

    LCM of 21, 35 and 45 is equal to 315. The comprehensive work provides more insight of how to find what is the lcm of 21, 35 and 45 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 21, 35 and 45?
    lcm (21   35   45) = (?)
    21 => 3 x 7
    35 => 5 x 7
    45 => 3 x 3 x 5

    = 3 x 5 x 7 x 3
    = 315
    lcm (21, 35 and 45) = 315
    315 is the lcm of 21, 35 and 45.

    where,
    21 is a positive integer,
    35 is a positive integer,
    315 is the lcm of 21, 35 and 45,
    {3, 5, 7} in {3 x 7, 5 x 7, 3 x 3 x 5} are the most repeated factors of 21, 35 and 45,
    {3} in {3 x 7, 5 x 7, 3 x 3 x 5} is the other remaining factors of 21, 35 and 45.

    Use in Mathematics: LCM of 21, 35 and 45
    The below are some of the mathematical applications where lcm of 21, 35 and 45 can be used:

    1. to find the least number which is exactly divisible by 21, 35 and 45.
    2. to find the common denominators for the fractions having 21, 35 and 45 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 21, 35 and 45 lcm
    In the context of lcm real world problems, the lcm of 21, 35 and 45 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 21 seconds, B tolls at 35 seconds and C tolls at 45 seconds repeatedly. The answer is that all bells A, B and C toll together at 315 seconds for the first time, at 630 seconds for the second time, at 945 seconds for the third time and so on.

    Important Notes: 21, 35 and 45 lcm
    The below are the important notes to be remembered while solving the lcm of 21, 35 and 45:
    1. The repeated and non-repeated prime factors of 21, 35 and 45 should be multiplied to find the least common multiple of 21, 35 and 45, when solving lcm by using prime factors method.
    2. The results of lcm of 21, 35 and 45 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 21, 35 and 45, use this below tool:

    How-to: What is the LCM of 21, 35 and 45?

    The below solved example with step by step work shows how to find what is the lcm of 21, 35 and 45 by using either prime factors method and special division method.

    Solved example using prime factors method:
    What is the LCM of 21, 35 and 45?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 21
    B = 35
    C = 45

    What to be found:
    find the lcm of 21, 35 and 45

    step 2 Find the prime factors of 21, 35 and 45:
    Prime factors of 21 = 3 x 7
    Prime factors of 35 = 5 x 7
    Prime factors of 45 = 3 x 3 x 5

    step 3 Identify the repeated and non-repeated prime factors of 21, 35 and 45:
    {3, 5, 7} are the most repeated factors and {3} is the non-repeated factors of 21, 35 and 45.

    step 4 Find the product of repeated and non-repeated prime factors of 21, 35 and 45:
    = 3 x 5 x 7 x 3
    = 315
    lcm(20 and 30) = 315

    Hence,
    lcm of 21, 35 and 45 is 315


    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 21, 35 and 45.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 21, 35 and 45

    What to be found:
    lcm (21, 35, 45) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    21, 35 and 45

    step 3 Choose the divisor which divides each or most of the given integers (21, 35 and 45), 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 21, 35 and 45 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    3213545
    373515
    57355
    7771
    111

    step 4 Multiply the divisors to find the lcm of 21, 35 and 45:
    = 3 x 3 x 5 x 7
    = 315
    LCM(21, 35, 45) = 315

    The least common multiple for three numbers 21, 35 and 45 is 315
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