LCM of 100 and 105
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 100 and 105 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 2100 as output. Here you can check the answer for Find the LCM of 100 and 105.
What is LCM of 100 and 105
Given Numbers are 100, 105
We can find the LCM of 100, 105 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 100 and 105
Multiples of 100 =100,200,300,400,500,600,700,800,900,1000,1100,1200,1300,1400,1500,1600,1700,
Multiples of 105 =105,210,315,420,525,630,735,840,945,1050,1155,1260,1365,1470,1575,1680,1785,
Now, get the least common multiple of 100, 105 which is 2100
So, the LCM of 100, 105 is 2100.
Least Common Multiple (LCM) of 100 and 105 with the help of Prime Factorisation
One method for determining the LCM of 100 and 105 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 100's prime factorization:
| 2 | 100 |
| 2 | 50 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 100 are 2,5.
100 = 22×52
And this is 105's prime factorization:
| 3 | 105 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 105 are 3, 5,7.
105 = 31×51×71
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: 2,5, 3,7
.22×31×52×71 = 2100
This shows that the LCM of 100 and 105 is 2100.
How to Calculate the LCM of 100 and 105 Using Common Multiples
The first step in determining the Least Common Multiple of 100 and 105 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 100 and 105:
Lets look at the first ten multiples of these numbers, 100 and 105:
100,200,300,400,500,600,700,800,900,1700 are the first ten multiples of 100.
105,210,315,420,525,630,735,840,945,1785 are the first ten multiples of 105.
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 100 and 105, for example, are 1200, 1700, and 1680. 2100 is the least common multiple since it is the smallest.
100 and 105 have an LCM of 2100.
Least Common Multiple of 100 and 105 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 100 and 105, than apply into the LCM equation.
GCF(100,105) = 5
LCM(100,105) = ( 100 × 105) / 5
LCM(100,105) = 10500 / 5
LCM(100,105) = 2100
Related Least Common Multiples of 100
Related Least Common Multiples of 105
Frequently Asked Questions on LCM of 100 and 105
1. What is the LCM of 100 and 105?
The LCM of 100 and 105 is 2100.
2. How to find the lowest common multiple of 100 and 105?
To find the lowest common multiple of 100 and 105, we have to get the multip;es of both numbers and identify the least common multiple in them which is 2100.
3. What are the Factors of 100?
Answer: Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. There are 9 integers that are factors of 100. The greatest factor of 100 is 100.
4. 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.
5. How to Find the LCM of 100 and 105?Answer:
Least Common Multiple of 100 and 105 = 2100
Step 1: Find the prime factorization of 100
100 = 2 x 2 x 5 x 5
Step 2: Find the prime factorization of 105
105 = 3 x 5 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 = 2100 = 2 x 2 x 3 x 5 x 5 x 7
Step 4: Therefore, the least common multiple of 100 and 105 is 2100.