LCM of 105 and 112
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 105 and 112 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 1680 as output. Here you can check the answer for Find the LCM of 105 and 112.
What is LCM of 105 and 112
Given Numbers are 105, 112
We can find the LCM of 105, 112 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 105 and 112
Multiples of 105 =105,210,315,420,525,630,735,840,945,1050,1155,1260,1365,1470,1575,1680,1785,
Multiples of 112 =112,224,336,448,560,672,784,896,1008,1120,1232,1344,1456,1568,1680,1792,1904,
Now, get the least common multiple of 105, 112 which is 1680
So, the LCM of 105, 112 is 1680.
Least Common Multiple (LCM) of 105 and 112 with the help of Prime Factorisation
One method for determining the LCM of 105 and 112 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 112's prime factorization:
| 2 | 112 |
| 2 | 56 |
| 2 | 28 |
| 2 | 14 |
| 7 | 7 |
| 1 |
Prime factors of 112 are 2,7.
112 = 24×71
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, 5,7,2
.24×31×51×71 = 1680
This shows that the LCM of 105 and 112 is 1680.
How to Calculate the LCM of 105 and 112 Using Common Multiples
The first step in determining the Least Common Multiple of 105 and 112 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 105 and 112:
Lets look at the first ten multiples of these numbers, 105 and 112:
105,210,315,420,525,630,735,840,945,1785 are the first ten multiples of 105.
112,224,336,448,560,672,784,896,1008,1904 are the first ten multiples of 112.
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 112, for example, are 1260, 1785, and 1792. 1680 is the least common multiple since it is the smallest.
105 and 112 have an LCM of 1680.
Least Common Multiple of 105 and 112 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 112, than apply into the LCM equation.
GCF(105,112) = 7
LCM(105,112) = ( 105 × 112) / 7
LCM(105,112) = 11760 / 7
LCM(105,112) = 1680
Related Least Common Multiples of 105
Related Least Common Multiples of 112
Frequently Asked Questions on LCM of 105 and 112
1. What is the LCM of 105 and 112?
The LCM of 105 and 112 is 1680.
2. How to find the lowest common multiple of 105 and 112?
To find the lowest common multiple of 105 and 112, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1680.
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 112?
Answer: Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112. There are 10 integers that are factors of 112. The greatest factor of 112 is 112.
5. How to Find the LCM of 105 and 112?Answer:
Least Common Multiple of 105 and 112 = 1680
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 112
112 = 2 x 2 x 2 x 2 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 = 1680 = 2 x 2 x 2 x 2 x 3 x 5 x 7
Step 4: Therefore, the least common multiple of 105 and 112 is 1680.