find the HCF and LCM 53,19
Answers
Answer:
The lcm of 53 and 19 is the smallest positive integer that divides the numbers 53 and 19 without a remainder. Spelled out, it is the least common multiple of 53 and 19. Here you can find the lcm of 53 and 19, 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 53 and 19, but also that of three or more integers including fifty-three and nineteen for example. Keep reading to learn everything about the lcm (53,19) and the terms related to it.
What is the LCM of 53 and 19
If you just want to know what is the least common multiple of 53 and 19, it is 1007. Usually, this is written as
lcm(53,19) = 1007
The lcm of 53 and 19 can be obtained like this:
The multiples of 53 are … , 954, 1007, 1060, ….
The multiples of 19 are …, 988, 1007, 1026, …
The common multiples of 53 and 19 are n x 1007, intersecting the two sets above, n\neq 0 \thinspace\in\thinspace\mathbb{Z}n
=0∈Z.
In the intersection multiples of 53 ∩ multiples of 19 the least positive element is 1007.
Therefore, the least common multiple of 53 and 19 is 1007.
Taking the above into account you also know how to find all the common multiples of 53 and 19, not just the smallest. In the next section we show you how to calculate the lcm of fifty-three and nineteen by means of two more methods.
How to find the LCM of 53 and 19
The least common multiple of 53 and 19 can be computed by using the greatest common factor aka gcf of 53 and 19. This is the easiest approach:
lcm (53,19) = \frac{53 \times 19}{gcf(53,19)} = \frac{1007}{1}
gcf(53,19)
53×19
=
1
1007
= 1007
Alternatively, the lcm of 53 and 19 can be found using the prime factorization of 53 and 19:
The prime factorization of 53 is: 53
The prime factorization of 19 is: 19
Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(53,53) = 1007
In any case, the easiest way to compute the lcm of two numbers like 53 and 19 is by using our calculator below. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 53,19. Push the button only to start over.
Answer:
The first step to find the gcf of 19 and 53 is to list the factors of each number. The factors of 19 are 1 and 19. The factors of 53 are 1 and 53. So, the Greatest Common Factor for these numbers is 1 because it divides all them without a remainder.
What is the LCM of 53 and 19
If you just want to know what is the least common multiple of 53 and 19, it is 1007. Usually, this is written as
lcm(53,19) = 1007