Calculators & Converters

    102 and 105 LCM

    LCM - Least Common Multiple Calculator

    LCM of 102 and 105 is equal to 3570. The comprehensive work provides more insight of how to find what is the lcm of 102 and 105 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 102 and 105?
    lcm (102   105) = (?)
    102 => 2 x 3 x 17
    105 => 3 x 5 x 7

    = 3 x 2 x 17 x 5 x 7
    = 3570
    lcm (102 and 105) = 3570
    3570 is the lcm of 102 and 105.

    where,
    102 is a positive integer,
    105 is a positive integer,
    3570 is the lcm of 102 and 105,
    {3} in {2 x 3 x 17, 3 x 5 x 7} is the common factors of 102 and 105,
    {2 x 17 x 5 x 7} in {2 x 3 x 17, 3 x 5 x 7} are the uncommon factors of 102 and 105.

    Use in Mathematics: LCM of 102 and 105
    The below are some of the mathematical applications where lcm of 102 and 105 can be used:

    1. to find the least number which is exactly divisible by 102 and 105.
    2. to find the common denominator for two fractions having 102 and 105 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 102 and 105 lcm
    In the context of lcm real world problems, the lcm of 102 and 105 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 102 seconds and bell B tolls at 105 seconds repeatedly. The answer is that all bells A and B toll together at 3570 seconds for the first time, at 7140 seconds for the second time, at 10710 seconds for the third time and so on.

    Important Notes: 102 and 105 lcm
    The below are the important notes to be remembered while solving the lcm of 102 and 105:
    1. The common prime factors and the remaining prime factors of 102 and 105 should be multiplied to find the least common multiple of 102 and 105, when solving lcm by using prime factors method.
    2. The results of lcm of 102 and 105, and the lcm of 105 and 102 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
    For values other than 102 and 105, use this below tool:

    How-to: What is the LCM of 102 and 105?

    The below solved example with step by step work shows how to find what is the lcm of 102 and 105 by using prime factors method and division method.

    Solved example using prime factors method:
    What is the LCM of 102 and 105?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 102
    B = 105

    What to be found:
    find the lcm of 102 and 105

    step 2 Find the prime factors of 102 and 105:
    Prime factors of 102 = 2 x 3 x 17
    Prime factors of 105 = 3 x 5 x 7

    step 3 Identify the repeated and non-repeated prime factors of 102 and 105:
    {3} is the most repeated factor and {2 x 17 x 5 x 7} are the non-repeated factors of 102 and 105.

    step 4 Find the product of repeated and non-repeated prime factors of 102 and 105:
    = 3 x 2 x 17 x 5 x 7
    = 3570
    lcm(102 and 105) = 3570

    Hence,
    lcm of 102 and 105 is 3570


    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 102 and 105.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 102 and 105

    What to be found:
    lcm (102, 105) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    102 and 105

    step 3 Choose the divisor which divides each or most of the given integers (102 and 105), 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 102 and 105 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    2102105
    351105
    51735
    7177
    17171
    11

    step 4 Multiply the divisors to find the lcm of 102 and 105:
    = 2 x 3 x 5 x 7 x 17
    = 3570
    LCM(102, 105) = 3570

    The least common multiple for two numbers 102 and 105 is 3570
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