Calculators & Converters

    34 and 66 LCM

    LCM - Least Common Multiple Calculator

    LCM of 34 and 66 is equal to 1122. The comprehensive work provides more insight of how to find what is the lcm of 34 and 66 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 and 66?
    lcm (34   66) = (?)
    34 => 2 x 17
    66 => 2 x 3 x 11

    = 2 x 17 x 3 x 11
    = 1122
    lcm (34 and 66) = 1122
    1122 is the lcm of 34 and 66.

    where,
    34 is a positive integer,
    66 is a positive integer,
    1122 is the lcm of 34 and 66,
    {2} in {2 x 17, 2 x 3 x 11} is the common factors of 34 and 66,
    {17 x 3 x 11} in {2 x 17, 2 x 3 x 11} are the uncommon factors of 34 and 66.

    Use in Mathematics: LCM of 34 and 66
    The below are some of the mathematical applications where lcm of 34 and 66 can be used:

    1. to find the least number which is exactly divisible by 34 and 66.
    2. to find the common denominator for two fractions having 34 and 66 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 34 and 66 lcm
    In the context of lcm real world problems, the lcm of 34 and 66 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 34 seconds and bell B tolls at 66 seconds repeatedly. The answer is that all bells A and B toll together at 1122 seconds for the first time, at 2244 seconds for the second time, at 3366 seconds for the third time and so on.

    Important Notes: 34 and 66 lcm
    The below are the important notes to be remembered while solving the lcm of 34 and 66:
    1. The common prime factors and the remaining prime factors of 34 and 66 should be multiplied to find the least common multiple of 34 and 66, when solving lcm by using prime factors method.
    2. The results of lcm of 34 and 66, and the lcm of 66 and 34 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
    For values other than 34 and 66, use this below tool:

    How-to: What is the LCM of 34 and 66?

    The below solved example with step by step work shows how to find what is the lcm of 34 and 66 by using prime factors method and division method.

    Solved example using prime factors method:
    What is the LCM of 34 and 66?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 34
    B = 66

    What to be found:
    find the lcm of 34 and 66

    step 2 Find the prime factors of 34 and 66:
    Prime factors of 34 = 2 x 17
    Prime factors of 66 = 2 x 3 x 11

    step 3 Identify the repeated and non-repeated prime factors of 34 and 66:
    {2} is the most repeated factor and {17 x 3 x 11} are the non-repeated factors of 34 and 66.

    step 4 Find the product of repeated and non-repeated prime factors of 34 and 66:
    = 2 x 17 x 3 x 11
    = 1122
    lcm(34 and 66) = 1122

    Hence,
    lcm of 34 and 66 is 1122


    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 and 66.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 34 and 66

    What to be found:
    lcm (34, 66) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    34 and 66

    step 3 Choose the divisor which divides each or most of the given integers (34 and 66), 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 and 66 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    23466
    31733
    111711
    17171
    11

    step 4 Multiply the divisors to find the lcm of 34 and 66:
    = 2 x 3 x 11 x 17
    = 1122
    LCM(34, 66) = 1122

    The least common multiple for two numbers 34 and 66 is 1122
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