Calculators & Converters

    16 and 56 LCM

    LCM - Least Common Multiple Calculator

    LCM of 16 and 56 is equal to 112. The comprehensive work provides more insight of how to find what is the lcm of 16 and 56 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

    what is the lcm of 16 and 56?
    lcm (16   56) = (?)
    16 => 2 x 2 x 2 x 2
    56 => 2 x 2 x 2 x 7

    = 2 x 2 x 2 x 2 x 7
    = 112
    lcm (16 and 56) = 112
    112 is the lcm of 16 and 56.

    where,
    16 is a positive integer,
    56 is a positive integer,
    112 is the lcm of 16 and 56,
    {2 x 2 x 2} in {2 x 2 x 2 x 2, 2 x 2 x 2 x 7} are the common factors of 16 and 56,
    {2 x 7} in {2 x 2 x 2 x 2, 2 x 2 x 2 x 7} are the uncommon factors of 16 and 56.

    Use in Mathematics: LCM of 16 and 56
    The below are some of the mathematical applications where lcm of 16 and 56 can be used:

    1. to find the least number which is exactly divisible by 16 and 56.
    2. to find the common denominator for two fractions having 16 and 56 as denominators in the unlike fractions addition or subtraction.
    Use in Real-world Problems: 16 and 56 lcm
    In the context of lcm real world problems, the lcm of 16 and 56 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 16 seconds and bell B tolls at 56 seconds repeatedly. The answer is that all bells A and B toll together at 112 seconds for the first time, at 224 seconds for the second time, at 336 seconds for the third time and so on.

    Important Notes: 16 and 56 lcm
    The below are the important notes to be remembered while solving the lcm of 16 and 56:
    1. The common prime factors and the remaining prime factors of 16 and 56 should be multiplied to find the least common multiple of 16 and 56, when solving lcm by using prime factors method.
    2. The results of lcm of 16 and 56, and the lcm of 56 and 16 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
    For values other than 16 and 56, use this below tool:

    How-to: What is the LCM of 16 and 56?

    The below solved example with step by step work shows how to find what is the lcm of 16 and 56 by using prime factors method and division method.

    Solved example using prime factors method:
    What is the LCM of 16 and 56?

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    A = 16
    B = 56

    What to be found:
    find the lcm of 16 and 56

    step 2 Find the prime factors of 16 and 56:
    Prime factors of 16 = 2 x 2 x 2 x 2
    Prime factors of 56 = 2 x 2 x 2 x 7

    step 3 Identify the repeated and non-repeated prime factors of 16 and 56:
    {2, 2, 2} are the most repeated factors and {2 x 7} are the non-repeated factors of 16 and 56.

    step 4 Find the product of repeated and non-repeated prime factors of 16 and 56:
    = 2 x 2 x 2 x 2 x 7
    = 112
    lcm(16 and 56) = 112

    Hence,
    lcm of 16 and 56 is 112


    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 16 and 56.

    step 1 Address the input parameters, values and observe what to be found:
    Input parameters and values:
    Integers: 16 and 56

    What to be found:
    lcm (16, 56) = ?

    step 2 Arrange the given integers in the horizontal form with space or comma separated format:
    16 and 56

    step 3 Choose the divisor which divides each or most of the given integers (16 and 56), 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 16 and 56 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

    21656
    2828
    2414
    227
    717
    11

    step 4 Multiply the divisors to find the lcm of 16 and 56:
    = 2 x 2 x 2 x 2 x 7
    = 112
    LCM(16, 56) = 112

    The least common multiple for two numbers 16 and 56 is 112
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