LCM of 63 and 68
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 63 and 68 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 4284 as output. Here you can check the answer for Find the LCM of 63 and 68.
What is LCM of 63 and 68
Given Numbers are 63, 68
We can find the LCM of 63, 68 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 63 and 68
Multiples of 63 =63,126,189,252,315,378,441,504,567,630,693,756,819,882,945,1008,1071,
Multiples of 68 =68,136,204,272,340,408,476,544,612,680,748,816,884,952,1020,1088,1156,
Now, get the least common multiple of 63, 68 which is 4284
So, the LCM of 63, 68 is 4284.
Least Common Multiple (LCM) of 63 and 68 with the help of Prime Factorisation
One method for determining the LCM of 63 and 68 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 63's prime factorization:
| 3 | 63 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 63 are 3,7.
63 = 32×71
And this is 68's prime factorization:
| 2 | 68 |
| 2 | 34 |
| 17 | 17 |
| 1 |
Prime factors of 68 are 2,17.
68 = 22×171
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 3,7, 2,17
.22×32×71×171 = 4284
This shows that the LCM of 63 and 68 is 4284.
How to Calculate the LCM of 63 and 68 Using Common Multiples
The first step in determining the Least Common Multiple of 63 and 68 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 63 and 68:
Lets look at the first ten multiples of these numbers, 63 and 68:
63,126,189,252,315,378,441,504,567,1071 are the first ten multiples of 63.
68,136,204,272,340,408,476,544,612,1156 are the first ten multiples of 68.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 63 and 68, for example, are 756, 1071, and 1088. 4284 is the least common multiple since it is the smallest.
63 and 68 have an LCM of 4284.
Least Common Multiple of 63 and 68 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 63 and 68, than apply into the LCM equation.
GCF(63,68) = 1
LCM(63,68) = ( 63 × 68) / 1
LCM(63,68) = 4284 / 1
LCM(63,68) = 4284
Related Least Common Multiples of 63
Related Least Common Multiples of 68
Frequently Asked Questions on LCM of 63 and 68
1. What is the LCM of 63 and 68?
The LCM of 63 and 68 is 4284.
2. How to find the lowest common multiple of 63 and 68?
To find the lowest common multiple of 63 and 68, we have to get the multip;es of both numbers and identify the least common multiple in them which is 4284.
3. What are the Factors of 63?
Answer: Factors of 63 are 1, 3, 7, 9, 21, 63. There are 6 integers that are factors of 63. The greatest factor of 63 is 63.
4. What are the Factors of 68?
Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.
5. How to Find the LCM of 63 and 68?Answer:
Least Common Multiple of 63 and 68 = 4284
Step 1: Find the prime factorization of 63
63 = 3 x 3 x 7
Step 2: Find the prime factorization of 68
68 = 2 x 2 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4284 = 2 x 2 x 3 x 3 x 7 x 17
Step 4: Therefore, the least common multiple of 63 and 68 is 4284.