LCM of 105 and 110
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 105 and 110 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 2310 as output. Here you can check the answer for Find the LCM of 105 and 110.
What is LCM of 105 and 110
Given Numbers are 105, 110
We can find the LCM of 105, 110 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 105 and 110
Multiples of 105 =105,210,315,420,525,630,735,840,945,1050,1155,1260,1365,1470,1575,1680,1785,
Multiples of 110 =110,220,330,440,550,660,770,880,990,1100,1210,1320,1430,1540,1650,1760,1870,
Now, get the least common multiple of 105, 110 which is 2310
So, the LCM of 105, 110 is 2310.
Least Common Multiple (LCM) of 105 and 110 with the help of Prime Factorisation
One method for determining the LCM of 105 and 110 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 105's prime factorization:
| 3 | 105 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 105 are 3, 5,7.
105 = 31×51×71
And this is 110's prime factorization:
| 2 | 110 |
| 5 | 55 |
| 11 | 11 |
| 1 |
Prime factors of 110 are 2, 5,11.
110 = 21×51×111
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: 3, 5,7, 2,11
.21×31×51×71×111 = 2310
This shows that the LCM of 105 and 110 is 2310.
How to Calculate the LCM of 105 and 110 Using Common Multiples
The first step in determining the Least Common Multiple of 105 and 110 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 105 and 110:
Lets look at the first ten multiples of these numbers, 105 and 110:
105,210,315,420,525,630,735,840,945,1785 are the first ten multiples of 105.
110,220,330,440,550,660,770,880,990,1870 are the first ten multiples of 110.
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 105 and 110, for example, are 1260, 1785, and 1760. 2310 is the least common multiple since it is the smallest.
105 and 110 have an LCM of 2310.
Least Common Multiple of 105 and 110 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 105 and 110, than apply into the LCM equation.
GCF(105,110) = 5
LCM(105,110) = ( 105 × 110) / 5
LCM(105,110) = 11550 / 5
LCM(105,110) = 2310
Related Least Common Multiples of 105
Related Least Common Multiples of 110
Frequently Asked Questions on LCM of 105 and 110
1. What is the LCM of 105 and 110?
The LCM of 105 and 110 is 2310.
2. How to find the lowest common multiple of 105 and 110?
To find the lowest common multiple of 105 and 110, we have to get the multip;es of both numbers and identify the least common multiple in them which is 2310.
3. What are the Factors of 105?
Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.
4. 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.
5. How to Find the LCM of 105 and 110?Answer:
Least Common Multiple of 105 and 110 = 2310
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 110
110 = 2 x 5 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 = 2310 = 2 x 3 x 5 x 7 x 11
Step 4: Therefore, the least common multiple of 105 and 110 is 2310.