LCM of 98 and 102
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 98 and 102 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 4998 as output. Here you can check the answer for Find the LCM of 98 and 102.
What is LCM of 98 and 102
Given Numbers are 98, 102
We can find the LCM of 98, 102 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 98 and 102
Multiples of 98 =98,196,294,392,490,588,686,784,882,980,1078,1176,1274,1372,1470,1568,1666,
Multiples of 102 =102,204,306,408,510,612,714,816,918,1020,1122,1224,1326,1428,1530,1632,1734,
Now, get the least common multiple of 98, 102 which is 4998
So, the LCM of 98, 102 is 4998.
Least Common Multiple (LCM) of 98 and 102 with the help of Prime Factorisation
One method for determining the LCM of 98 and 102 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 98's prime factorization:
| 2 | 98 |
| 7 | 49 |
| 7 | 7 |
| 1 |
Prime factors of 98 are 2,7.
98 = 21×72
And this is 102's prime factorization:
| 2 | 102 |
| 3 | 51 |
| 17 | 17 |
| 1 |
Prime factors of 102 are 2, 3,17.
102 = 21×31×171
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: 2,7, 3,17
.21×31×72×171 = 4998
This shows that the LCM of 98 and 102 is 4998.
How to Calculate the LCM of 98 and 102 Using Common Multiples
The first step in determining the Least Common Multiple of 98 and 102 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 98 and 102:
Lets look at the first ten multiples of these numbers, 98 and 102:
98,196,294,392,490,588,686,784,882,1666 are the first ten multiples of 98.
102,204,306,408,510,612,714,816,918,1734 are the first ten multiples of 102.
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 98 and 102, for example, are 1176, 1666, and 1632. 4998 is the least common multiple since it is the smallest.
98 and 102 have an LCM of 4998.
Least Common Multiple of 98 and 102 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 98 and 102, than apply into the LCM equation.
GCF(98,102) = 2
LCM(98,102) = ( 98 × 102) / 2
LCM(98,102) = 9996 / 2
LCM(98,102) = 4998
Related Least Common Multiples of 98
Related Least Common Multiples of 102
Frequently Asked Questions on LCM of 98 and 102
1. What is the LCM of 98 and 102?
The LCM of 98 and 102 is 4998.
2. How to find the lowest common multiple of 98 and 102?
To find the lowest common multiple of 98 and 102, we have to get the multip;es of both numbers and identify the least common multiple in them which is 4998.
3. What are the Factors of 98?
Answer: Factors of 98 are 1, 2, 7, 14, 49, 98. There are 6 integers that are factors of 98. The greatest factor of 98 is 98.
4. What are the Factors of 102?
Answer: Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. There are 8 integers that are factors of 102. The greatest factor of 102 is 102.
5. How to Find the LCM of 98 and 102?Answer:
Least Common Multiple of 98 and 102 = 4998
Step 1: Find the prime factorization of 98
98 = 2 x 7 x 7
Step 2: Find the prime factorization of 102
102 = 2 x 3 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 = 4998 = 2 x 3 x 7 x 7 x 17
Step 4: Therefore, the least common multiple of 98 and 102 is 4998.