LCM of 84 and 88
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 84 and 88 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 1848 as output. Here you can check the answer for Find the LCM of 84 and 88.
What is LCM of 84 and 88
Given Numbers are 84, 88
We can find the LCM of 84, 88 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 84 and 88
Multiples of 84 =84,168,252,336,420,504,588,672,756,840,924,1008,1092,1176,1260,1344,1428,
Multiples of 88 =88,176,264,352,440,528,616,704,792,880,968,1056,1144,1232,1320,1408,1496,
Now, get the least common multiple of 84, 88 which is 1848
So, the LCM of 84, 88 is 1848.
Least Common Multiple (LCM) of 84 and 88 with the help of Prime Factorisation
One method for determining the LCM of 84 and 88 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 84's prime factorization:
| 2 | 84 |
| 2 | 42 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 84 are 2, 3,7.
84 = 22×31×71
And this is 88's prime factorization:
| 2 | 88 |
| 2 | 44 |
| 2 | 22 |
| 11 | 11 |
| 1 |
Prime factors of 88 are 2,11.
88 = 23×111
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: 2, 3,7,11
.23×31×71×111 = 1848
This shows that the LCM of 84 and 88 is 1848.
How to Calculate the LCM of 84 and 88 Using Common Multiples
The first step in determining the Least Common Multiple of 84 and 88 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 84 and 88:
Lets look at the first ten multiples of these numbers, 84 and 88:
84,168,252,336,420,504,588,672,756,1428 are the first ten multiples of 84.
88,176,264,352,440,528,616,704,792,1496 are the first ten multiples of 88.
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 84 and 88, for example, are 1008, 1428, and 1408. 1848 is the least common multiple since it is the smallest.
84 and 88 have an LCM of 1848.
Least Common Multiple of 84 and 88 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84 and 88, than apply into the LCM equation.
GCF(84,88) = 4
LCM(84,88) = ( 84 × 88) / 4
LCM(84,88) = 7392 / 4
LCM(84,88) = 1848
Related Least Common Multiples of 84
Related Least Common Multiples of 88
Frequently Asked Questions on LCM of 84 and 88
1. What is the LCM of 84 and 88?
The LCM of 84 and 88 is 1848.
2. How to find the lowest common multiple of 84 and 88?
To find the lowest common multiple of 84 and 88, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1848.
3. What are the Factors of 84?
Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.
4. What are the Factors of 88?
Answer: Factors of 88 are 1, 2, 4, 8, 11, 22, 44, 88. There are 8 integers that are factors of 88. The greatest factor of 88 is 88.
5. How to Find the LCM of 84 and 88?Answer:
Least Common Multiple of 84 and 88 = 1848
Step 1: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
Step 2: Find the prime factorization of 88
88 = 2 x 2 x 2 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1848 = 2 x 2 x 2 x 3 x 7 x 11
Step 4: Therefore, the least common multiple of 84 and 88 is 1848.