LCM of 78 and 84
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 78 and 84 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 1092 as output. Here you can check the answer for Find the LCM of 78 and 84.
What is LCM of 78 and 84
Given Numbers are 78, 84
We can find the LCM of 78, 84 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 78 and 84
Multiples of 78 =78,156,234,312,390,468,546,624,702,780,858,936,1014,1092,1170,1248,1326,
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 78, 84 which is 1092
So, the LCM of 78, 84 is 1092.
Least Common Multiple (LCM) of 78 and 84 with the help of Prime Factorisation
One method for determining the LCM of 78 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 78's prime factorization:
| 2 | 78 |
| 3 | 39 |
| 13 | 13 |
| 1 |
Prime factors of 78 are 2, 3,13.
78 = 21×31×131
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: 2, 3,13,7
.22×31×71×131 = 1092
This shows that the LCM of 78 and 84 is 1092.
How to Calculate the LCM of 78 and 84 Using Common Multiples
The first step in determining the Least Common Multiple of 78 and 84 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 78 and 84:
Lets look at the first ten multiples of these numbers, 78 and 84:
78,156,234,312,390,468,546,624,702,1326 are the first ten multiples of 78.
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 78 and 84, for example, are 936, 1326, and 1344. 1092 is the least common multiple since it is the smallest.
78 and 84 have an LCM of 1092.
Least Common Multiple of 78 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 78 and 84, than apply into the LCM equation.
GCF(78,84) = 6
LCM(78,84) = ( 78 × 84) / 6
LCM(78,84) = 6552 / 6
LCM(78,84) = 1092
Related Least Common Multiples of 78
Related Least Common Multiples of 84
Frequently Asked Questions on LCM of 78 and 84
1. What is the LCM of 78 and 84?
The LCM of 78 and 84 is 1092.
2. How to find the lowest common multiple of 78 and 84?
To find the lowest common multiple of 78 and 84, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1092.
3. What are the Factors of 78?
Answer: Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78. There are 8 integers that are factors of 78. The greatest factor of 78 is 78.
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 78 and 84?Answer:
Least Common Multiple of 78 and 84 = 1092
Step 1: Find the prime factorization of 78
78 = 2 x 3 x 13
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 = 1092 = 2 x 2 x 3 x 7 x 13
Step 4: Therefore, the least common multiple of 78 and 84 is 1092.