Calculators & Converters

    34, 51 and 68 LCM

    LCM - Least Common Multiple Calculator

    LCM of 34, 51 and 68 is equal to 204. The comprehensive work provides more insight of how to find what is the lcm of 34, 51 and 68 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 34, 51 and 68?
    lcm (34   51   68) = (?)
    34 => 2 x 17
    51 => 3 x 17
    68 => 2 x 2 x 17

    = 2 x 17 x 3 x 2
    = 204
    lcm (34, 51 and 68) = 204
    204 is the lcm of 34, 51 and 68.

    where,
    34 is a positive integer,
    51 is a positive integer,
    204 is the lcm of 34, 51 and 68,
    {2, 17} in {2 x 17, 3 x 17, 2 x 2 x 17} are the most repeated factors of 34, 51 and 68,
    {3, 2} in {2 x 17, 3 x 17, 2 x 2 x 17} are the the other remaining factors of 34, 51 and 68.

    Use in Mathematics: LCM of 34, 51 and 68
    The below are some of the mathematical applications where lcm of 34, 51 and 68 can be used:

    1. to find the least number which is exactly divisible by 34, 51 and 68.
    2. to find the common denominators for the fractions having 34, 51 and 68 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 34, 51 and 68 lcm
    In the context of lcm real world problems, the lcm of 34, 51 and 68 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 34 seconds, B tolls at 51 seconds and C tolls at 68 seconds repeatedly. The answer is that all bells A, B and C toll together at 204 seconds for the first time, at 408 seconds for the second time, at 612 seconds for the third time and so on.

    Important Notes: 34, 51 and 68 lcm
    The below are the important notes to be remembered while solving the lcm of 34, 51 and 68:
    1. The repeated and non-repeated prime factors of 34, 51 and 68 should be multiplied to find the least common multiple of 34, 51 and 68, when solving lcm by using prime factors method.
    2. The results of lcm of 34, 51 and 68 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 34, 51 and 68, use this below tool:

    How-to: What is the LCM of 34, 51 and 68?

    The below solved example with step by step work shows how to find what is the lcm of 34, 51 and 68 by using either prime factors method and special division method.

    Solved example using prime factors method:
    What is the LCM of 34, 51 and 68?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 34
    B = 51
    C = 68

    What to be found:
    find the lcm of 34, 51 and 68

    step 2 Find the prime factors of 34, 51 and 68:
    Prime factors of 34 = 2 x 17
    Prime factors of 51 = 3 x 17
    Prime factors of 68 = 2 x 2 x 17

    step 3 Identify the repeated and non-repeated prime factors of 34, 51 and 68:
    {2, 17} are the most repeated factors and {3, 2} are the non-repeated factors of 34, 51 and 68.

    step 4 Find the product of repeated and non-repeated prime factors of 34, 51 and 68:
    = 2 x 17 x 3 x 2
    = 204
    lcm(20 and 30) = 204

    Hence,
    lcm of 34, 51 and 68 is 204


    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 34, 51 and 68.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 34, 51 and 68

    What to be found:
    lcm (34, 51, 68) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    34, 51 and 68

    step 3 Choose the divisor which divides each or most of the given integers (34, 51 and 68), 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 34, 51 and 68 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    2345168
    2175134
    3175117
    17171717
    111

    step 4 Multiply the divisors to find the lcm of 34, 51 and 68:
    = 2 x 2 x 3 x 17
    = 204
    LCM(34, 51, 68) = 204

    The least common multiple for three numbers 34, 51 and 68 is 204
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