Calculators & Converters

    69 and 72 LCM

    LCM - Least Common Multiple Calculator

    LCM of 69 and 72 is equal to 1656. The comprehensive work provides more insight of how to find what is the lcm of 69 and 72 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 69 and 72?
    lcm (69   72) = (?)
    69 => 3 x 23
    72 => 2 x 2 x 2 x 3 x 3

    = 3 x 23 x 2 x 2 x 2 x 3
    = 1656
    lcm (69 and 72) = 1656
    1656 is the lcm of 69 and 72.

    where,
    69 is a positive integer,
    72 is a positive integer,
    1656 is the lcm of 69 and 72,
    {3} in {3 x 23, 2 x 2 x 2 x 3 x 3} is the common factors of 69 and 72,
    {23 x 2 x 2 x 2 x 3} in {3 x 23, 2 x 2 x 2 x 3 x 3} are the uncommon factors of 69 and 72.

    Use in Mathematics: LCM of 69 and 72
    The below are some of the mathematical applications where lcm of 69 and 72 can be used:

    1. to find the least number which is exactly divisible by 69 and 72.
    2. to find the common denominator for two fractions having 69 and 72 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 69 and 72 lcm
    In the context of lcm real world problems, the lcm of 69 and 72 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 69 seconds and bell B tolls at 72 seconds repeatedly. The answer is that all bells A and B toll together at 1656 seconds for the first time, at 3312 seconds for the second time, at 4968 seconds for the third time and so on.

    Important Notes: 69 and 72 lcm
    The below are the important notes to be remembered while solving the lcm of 69 and 72:
    1. The common prime factors and the remaining prime factors of 69 and 72 should be multiplied to find the least common multiple of 69 and 72, when solving lcm by using prime factors method.
    2. The results of lcm of 69 and 72, and the lcm of 72 and 69 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
    For values other than 69 and 72, use this below tool:

    How-to: What is the LCM of 69 and 72?

    The below solved example with step by step work shows how to find what is the lcm of 69 and 72 by using prime factors method and division method.

    Solved example using prime factors method:
    What is the LCM of 69 and 72?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 69
    B = 72

    What to be found:
    find the lcm of 69 and 72

    step 2 Find the prime factors of 69 and 72:
    Prime factors of 69 = 3 x 23
    Prime factors of 72 = 2 x 2 x 2 x 3 x 3

    step 3 Identify the repeated and non-repeated prime factors of 69 and 72:
    {3} is the most repeated factor and {23 x 2 x 2 x 2 x 3} are the non-repeated factors of 69 and 72.

    step 4 Find the product of repeated and non-repeated prime factors of 69 and 72:
    = 3 x 23 x 2 x 2 x 2 x 3
    = 1656
    lcm(69 and 72) = 1656

    Hence,
    lcm of 69 and 72 is 1656


    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 69 and 72.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 69 and 72

    What to be found:
    lcm (69, 72) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    69 and 72

    step 3 Choose the divisor which divides each or most of the given integers (69 and 72), 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 69 and 72 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    26972
    26936
    26918
    3699
    3233
    23231
    11

    step 4 Multiply the divisors to find the lcm of 69 and 72:
    = 2 x 2 x 2 x 3 x 3 x 23
    = 1656
    LCM(69, 72) = 1656

    The least common multiple for two numbers 69 and 72 is 1656
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