LCM of 99 and 105
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 99 and 105 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 3465 as output. Here you can check the answer for Find the LCM of 99 and 105.
What is LCM of 99 and 105
Given Numbers are 99, 105
We can find the LCM of 99, 105 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 99 and 105
Multiples of 99 =99,198,297,396,495,594,693,792,891,990,1089,1188,1287,1386,1485,1584,1683,
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 99, 105 which is 3465
So, the LCM of 99, 105 is 3465.
Least Common Multiple (LCM) of 99 and 105 with the help of Prime Factorisation
One method for determining the LCM of 99 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 99's prime factorization:
| 3 | 99 |
| 3 | 33 |
| 11 | 11 |
| 1 |
Prime factors of 99 are 3,11.
99 = 32×111
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: 3,11, 5,7
.32×51×71×111 = 3465
This shows that the LCM of 99 and 105 is 3465.
How to Calculate the LCM of 99 and 105 Using Common Multiples
The first step in determining the Least Common Multiple of 99 and 105 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 99 and 105:
Lets look at the first ten multiples of these numbers, 99 and 105:
99,198,297,396,495,594,693,792,891,1683 are the first ten multiples of 99.
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 99 and 105, for example, are 1188, 1683, and 1680. 3465 is the least common multiple since it is the smallest.
99 and 105 have an LCM of 3465.
Least Common Multiple of 99 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 99 and 105, than apply into the LCM equation.
GCF(99,105) = 3
LCM(99,105) = ( 99 × 105) / 3
LCM(99,105) = 10395 / 3
LCM(99,105) = 3465
Related Least Common Multiples of 99
Related Least Common Multiples of 105
Frequently Asked Questions on LCM of 99 and 105
1. What is the LCM of 99 and 105?
The LCM of 99 and 105 is 3465.
2. How to find the lowest common multiple of 99 and 105?
To find the lowest common multiple of 99 and 105, we have to get the multip;es of both numbers and identify the least common multiple in them which is 3465.
3. What are the Factors of 99?
Answer: Factors of 99 are 1, 3, 9, 11, 33, 99. There are 6 integers that are factors of 99. The greatest factor of 99 is 99.
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 99 and 105?Answer:
Least Common Multiple of 99 and 105 = 3465
Step 1: Find the prime factorization of 99
99 = 3 x 3 x 11
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 = 3465 = 3 x 3 x 5 x 7 x 11
Step 4: Therefore, the least common multiple of 99 and 105 is 3465.