LCM of 77 and 84
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 77 and 84 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 924 as output. Here you can check the answer for Find the LCM of 77 and 84.
What is LCM of 77 and 84
Given Numbers are 77, 84
We can find the LCM of 77, 84 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 77 and 84
Multiples of 77 =77,154,231,308,385,462,539,616,693,770,847,924,1001,1078,1155,1232,1309,
Multiples of 84 =84,168,252,336,420,504,588,672,756,840,924,1008,1092,1176,1260,1344,1428,
Now, get the least common multiple of 77, 84 which is 924
So, the LCM of 77, 84 is 924.
Least Common Multiple (LCM) of 77 and 84 with the help of Prime Factorisation
One method for determining the LCM of 77 and 84 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 77's prime factorization:
| 7 | 77 |
| 11 | 11 |
| 1 |
Prime factors of 77 are 7,11.
77 = 71×111
And this 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
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: 7,11, 2,3
.22×31×71×111 = 924
This shows that the LCM of 77 and 84 is 924.
How to Calculate the LCM of 77 and 84 Using Common Multiples
The first step in determining the Least Common Multiple of 77 and 84 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 77 and 84:
Lets look at the first ten multiples of these numbers, 77 and 84:
77,154,231,308,385,462,539,616,693,1309 are the first ten multiples of 77.
84,168,252,336,420,504,588,672,756,1428 are the first ten multiples of 84.
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 77 and 84, for example, are 924, 1309, and 1344. 924 is the least common multiple since it is the smallest.
77 and 84 have an LCM of 924.
Least Common Multiple of 77 and 84 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 77 and 84, than apply into the LCM equation.
GCF(77,84) = 7
LCM(77,84) = ( 77 × 84) / 7
LCM(77,84) = 6468 / 7
LCM(77,84) = 924
Related Least Common Multiples of 77
Related Least Common Multiples of 84
Frequently Asked Questions on LCM of 77 and 84
1. What is the LCM of 77 and 84?
The LCM of 77 and 84 is 924.
2. How to find the lowest common multiple of 77 and 84?
To find the lowest common multiple of 77 and 84, we have to get the multip;es of both numbers and identify the least common multiple in them which is 924.
3. What are the Factors of 77?
Answer: Factors of 77 are 1, 7, 11, 77. There are 4 integers that are factors of 77. The greatest factor of 77 is 77.
4. 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.
5. How to Find the LCM of 77 and 84?Answer:
Least Common Multiple of 77 and 84 = 924
Step 1: Find the prime factorization of 77
77 = 7 x 11
Step 2: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 924 = 2 x 2 x 3 x 7 x 11
Step 4: Therefore, the least common multiple of 77 and 84 is 924.