Given Numbers are 112, 120

We can find the LCM of 112, 120 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 112 and 120

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

Multiples of 120 =120,240,360,480,600,720,840,960,1080,1200,1320,1440,1560,1680,1800,1920,2040,

Now, get the least common multiple of 112, 120 which is 1680

So, the LCM of 112, 120 is 1680.

One method for determining the LCM of 112 and 120 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 120's prime factorization:

Prime factors of 120 are 2, 3,5.

120 = 2³×3¹×5¹

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, 3,5

2⁴×3¹×5¹×7¹ = 1680

This shows that the LCM of 112 and 120 is 1680.

The first step in determining the Least Common Multiple of 112 and 120 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 112 and 120:

Lets look at the first ten multiples of these numbers, 112 and 120:

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

120,240,360,480,600,720,840,960,1080,2040 are the first ten multiples of 120.

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 120, for example, are 1344, 1904, and 1920. 1680 is the least common multiple since it is the smallest.

112 and 120 have an LCM of 1680.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 112 and 120, than apply into the LCM equation.

GCF(112,120) = 8
LCM(112,120) = ( 112 × 120) / 8
LCM(112,120) = 13440 / 8
LCM(112,120) = 1680

1. What is the LCM of 112 and 120?

The LCM of 112 and 120 is 1680.

2. How to find the lowest common multiple of 112 and 120?

To find the lowest common multiple of 112 and 120, 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 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 120?

Answer: Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There are 16 integers that are factors of 120. The greatest factor of 120 is 120.

Answer:

Least Common Multiple of 112 and 120 = 1680

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 120

120 = 2 x 2 x 2 x 3 x 5

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 112 and 120 is 1680.