Answer:
LCM of 54 and 56
The lcm of 54 and 56 is the smallest positive integer that divides the numbers 54 and 56 without a remainder. Spelled out, it is the least common multiple of 54 and 56. Here you can find the lcm of 54 and 56, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the lcm of 54 and 56, but also that of three or more integers including fifty-four and fifty-six for example. Keep reading to learn everything about the lcm (54,56) and the terms related to it.
What is the LCM of 54 and 56
If you just want to know what is the least common multiple of 54 and 56, it is 1512. Usually, this is written as
The lcm of 54 and 56 can be obtained like. this:
- The multiples of 54 are … , 1458, 1512, 1566, ….
- The multiples of 56 are …, 1456, 1512, 1568, …
- The common multiples of 54 and 56 are n x 1512, intersecting the two sets above, n\neq 0 \thinspace\in\thinspace\mathbb{Z}n
=0∈Z.
- In the intersection multiples of 54 ∩ multiples of 56 the least positive element is 1512.
Therefore, the least common multiple of 54 and 56 is 1512.
Taking the above into account you also know how to find all the common multiples of 54 and 56, not just the smallest. In the next section we show you how to calculate the lcm of fifty-four and fifty-six by means of two more methods.
How to find the LCM of 54 and 56
The least common multiple of 54 and 56 can be computed by using the greatest common factor aka gcf of 54 and 56. This is the easiest approach:
[tex]lcm \: (54 \: 56) \: = [/tex]
54 × 56. 3024
_____________= _______= 1512
gcf(54,56) 2
Alternatively, the lcm of 54 and 56 can be found using the prime factorization of 54 and 56:
- The prime factorization of 54 is: 2 x 3 x 3 x 3
- The prime factorization of 56 is: 2 x 2 x 2 x 7
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(54,54) = 1512
THE ANSWER IS 1512
HOPE IT'S HELP
