Given Numbers are 106, 112

We can find the LCM of 106, 112 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 106 and 112

Multiples of 106 =106,212,318,424,530,636,742,848,954,1060,1166,1272,1378,1484,1590,1696,1802,

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 106, 112 which is 5936

So, the LCM of 106, 112 is 5936.

One method for determining the LCM of 106 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 106's prime factorization:

Prime factors of 106 are 2,53.

106 = 2¹×53¹

And this is 112's prime factorization:

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: 2,53,7

2⁴×7¹×53¹ = 5936

This shows that the LCM of 106 and 112 is 5936.

The first step in determining the Least Common Multiple of 106 and 112 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 106 and 112:

Lets look at the first ten multiples of these numbers, 106 and 112:

106,212,318,424,530,636,742,848,954,1802 are the first ten multiples of 106.

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 106 and 112, for example, are 1272, 1802, and 1792. 5936 is the least common multiple since it is the smallest.

106 and 112 have an LCM of 5936.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 106 and 112, than apply into the LCM equation.

GCF(106,112) = 2
LCM(106,112) = ( 106 × 112) / 2
LCM(106,112) = 11872 / 2
LCM(106,112) = 5936

1. What is the LCM of 106 and 112?

The LCM of 106 and 112 is 5936.

2. How to find the lowest common multiple of 106 and 112?

To find the lowest common multiple of 106 and 112, we have to get the multip;es of both numbers and identify the least common multiple in them which is 5936.

3. What are the Factors of 106?

Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.

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.

Answer:

Least Common Multiple of 106 and 112 = 5936

Step 1: Find the prime factorization of 106

106 = 2 x 53

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 = 5936 = 2 x 2 x 2 x 2 x 7 x 53

Step 4: Therefore, the least common multiple of 106 and 112 is 5936.