Given Numbers are 112, 117

We can find the LCM of 112, 117 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 112 and 117

Multiples of 112 =112,224,336,448,560,672,784,896,1008,1120,1232,1344,1456,1568,1680,1792,1904,

Multiples of 117 =117,234,351,468,585,702,819,936,1053,1170,1287,1404,1521,1638,1755,1872,1989,

Now, get the least common multiple of 112, 117 which is 13104

So, the LCM of 112, 117 is 13104.

One method for determining the LCM of 112 and 117 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 112's prime factorization:

Prime factors of 112 are 2,7.

112 = 2⁴×7¹

And this is 117's prime factorization:

Prime factors of 117 are 3,13.

117 = 3²×13¹

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: 2,7, 3,13

2⁴×3²×7¹×13¹ = 13104

This shows that the LCM of 112 and 117 is 13104.

The first step in determining the Least Common Multiple of 112 and 117 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 112 and 117:

Lets look at the first ten multiples of these numbers, 112 and 117:

112,224,336,448,560,672,784,896,1008,1904 are the first ten multiples of 112.

117,234,351,468,585,702,819,936,1053,1989 are the first ten multiples of 117.

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 112 and 117, for example, are 1344, 1904, and 1872. 13104 is the least common multiple since it is the smallest.

112 and 117 have an LCM of 13104.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 112 and 117, than apply into the LCM equation.

GCF(112,117) = 1
LCM(112,117) = ( 112 × 117) / 1
LCM(112,117) = 13104 / 1
LCM(112,117) = 13104

1. What is the LCM of 112 and 117?

The LCM of 112 and 117 is 13104.

2. How to find the lowest common multiple of 112 and 117?

To find the lowest common multiple of 112 and 117, we have to get the multip;es of both numbers and identify the least common multiple in them which is 13104.

3. 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.

4. What are the Factors of 117?

Answer: Factors of 117 are 1, 3, 9, 13, 39, 117. There are 6 integers that are factors of 117. The greatest factor of 117 is 117.

Answer:

Least Common Multiple of 112 and 117 = 13104

Step 1: Find the prime factorization of 112

112 = 2 x 2 x 2 x 2 x 7

Step 2: Find the prime factorization of 117

117 = 3 x 3 x 13

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 13104 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 13

Step 4: Therefore, the least common multiple of 112 and 117 is 13104.