LCM of 110 and 114
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 110 and 114 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 6270 as output. Here you can check the answer for Find the LCM of 110 and 114.
What is LCM of 110 and 114
Given Numbers are 110, 114
We can find the LCM of 110, 114 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 110 and 114
Multiples of 110 =110,220,330,440,550,660,770,880,990,1100,1210,1320,1430,1540,1650,1760,1870,
Multiples of 114 =114,228,342,456,570,684,798,912,1026,1140,1254,1368,1482,1596,1710,1824,1938,
Now, get the least common multiple of 110, 114 which is 6270
So, the LCM of 110, 114 is 6270.
Least Common Multiple (LCM) of 110 and 114 with the help of Prime Factorisation
One method for determining the LCM of 110 and 114 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 110's prime factorization:
| 2 | 110 |
| 5 | 55 |
| 11 | 11 |
| 1 |
Prime factors of 110 are 2, 5,11.
110 = 21×51×111
And this is 114's prime factorization:
| 2 | 114 |
| 3 | 57 |
| 19 | 19 |
| 1 |
Prime factors of 114 are 2, 3,19.
114 = 21×31×191
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, 5,11, 3,19
.21×31×51×111×191 = 6270
This shows that the LCM of 110 and 114 is 6270.
How to Calculate the LCM of 110 and 114 Using Common Multiples
The first step in determining the Least Common Multiple of 110 and 114 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 110 and 114:
Lets look at the first ten multiples of these numbers, 110 and 114:
110,220,330,440,550,660,770,880,990,1870 are the first ten multiples of 110.
114,228,342,456,570,684,798,912,1026,1938 are the first ten multiples of 114.
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 110 and 114, for example, are 1320, 1870, and 1824. 6270 is the least common multiple since it is the smallest.
110 and 114 have an LCM of 6270.
Least Common Multiple of 110 and 114 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 110 and 114, than apply into the LCM equation.
GCF(110,114) = 2
LCM(110,114) = ( 110 × 114) / 2
LCM(110,114) = 12540 / 2
LCM(110,114) = 6270
Related Least Common Multiples of 110
Related Least Common Multiples of 114
Frequently Asked Questions on LCM of 110 and 114
1. What is the LCM of 110 and 114?
The LCM of 110 and 114 is 6270.
2. How to find the lowest common multiple of 110 and 114?
To find the lowest common multiple of 110 and 114, we have to get the multip;es of both numbers and identify the least common multiple in them which is 6270.
3. What are the Factors of 110?
Answer: Factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110. There are 8 integers that are factors of 110. The greatest factor of 110 is 110.
4. What are the Factors of 114?
Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.
5. How to Find the LCM of 110 and 114?Answer:
Least Common Multiple of 110 and 114 = 6270
Step 1: Find the prime factorization of 110
110 = 2 x 5 x 11
Step 2: Find the prime factorization of 114
114 = 2 x 3 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6270 = 2 x 3 x 5 x 11 x 19
Step 4: Therefore, the least common multiple of 110 and 114 is 6270.