Calculators & Converters

    6 and 9 LCM

    LCM - Least Common Multiple Calculator

    LCM of 6 and 9 is equal to 18. The comprehensive work provides more insight of how to find what is the lcm of 6 and 9 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 6 and 9?
    lcm (6   9) = (?)
    6 => 2 x 3
    9 => 3 x 3

    = 3 x 2 x 3
    = 18
    lcm (6 and 9) = 18
    18 is the lcm of 6 and 9.

    where,
    6 is a positive integer,
    9 is a positive integer,
    18 is the lcm of 6 and 9,
    {3} in {2 x 3, 3 x 3} is the common factors of 6 and 9,
    {2 x 3} in {2 x 3, 3 x 3} are the uncommon factors of 6 and 9.

    Use in Mathematics: LCM of 6 and 9
    The below are some of the mathematical applications where lcm of 6 and 9 can be used:

    1. to find the least number which is exactly divisible by 6 and 9.
    2. to find the common denominator for two fractions having 6 and 9 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 6 and 9 lcm
    In the context of lcm real world problems, the lcm of 6 and 9 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 6 seconds and bell B tolls at 9 seconds repeatedly. The answer is that all bells A and B toll together at 18 seconds for the first time, at 36 seconds for the second time, at 54 seconds for the third time and so on.

    Important Notes: 6 and 9 lcm
    The below are the important notes to be remembered while solving the lcm of 6 and 9:
    1. The common prime factors and the remaining prime factors of 6 and 9 should be multiplied to find the least common multiple of 6 and 9, when solving lcm by using prime factors method.
    2. The results of lcm of 6 and 9, and the lcm of 9 and 6 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
    For values other than 6 and 9, use this below tool:

    How-to: What is the LCM of 6 and 9?

    The below solved example with step by step work shows how to find what is the lcm of 6 and 9 by using prime factors method and division method.

    Solved example using prime factors method:
    What is the LCM of 6 and 9?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 6
    B = 9

    What to be found:
    find the lcm of 6 and 9

    step 2 Find the prime factors of 6 and 9:
    Prime factors of 6 = 2 x 3
    Prime factors of 9 = 3 x 3

    step 3 Identify the repeated and non-repeated prime factors of 6 and 9:
    {3} is the most repeated factor and {2 x 3} are the non-repeated factors of 6 and 9.

    step 4 Find the product of repeated and non-repeated prime factors of 6 and 9:
    = 3 x 2 x 3
    = 18
    lcm(6 and 9) = 18

    Hence,
    lcm of 6 and 9 is 18


    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 6 and 9.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 6 and 9

    What to be found:
    lcm (6, 9) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    6 and 9

    step 3 Choose the divisor which divides each or most of the given integers (6 and 9), 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 6 and 9 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    269
    339
    313
    11

    step 4 Multiply the divisors to find the lcm of 6 and 9:
    = 2 x 3 x 3
    = 18
    LCM(6, 9) = 18

    The least common multiple for two numbers 6 and 9 is 18
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