Least Common Multiple of 106 and 112

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 106 and 112 the smallest integer that is 5936 that is divisible by both numbers.

Least Common Multiple (LCM) of 106 and 112 is 5936.

LCM(106,112) = 5936

LCM of 106 and 112

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 106 and 112

LCM of 106 and 112 is 5936

Least common multiple can be found by multiplying the highest exponent prime factors of 106 and 112. First we will calculate the prime factors of 106 and 112.

Prime Factorization of 106


2 106
53 53
1

Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:

106 = 21×531

Prime Factorization of 112


2 112
2 56
2 28
2 14
7 7
1

Prime factors of 112 are 2,7. Prime factorization of 112 in exponential form is:

112 = 24×71

Now multiplying the highest exponent prime factors to calculate the LCM of 106 and 112.

LCM(106,112) = 24×71×531
LCM(106,112) = 5936

Factors of 106

List of positive integer factors of 106 that divides 106 without a remainder.

1, 2, 53, 106

Factors of 112

List of positive integer factors of 112 that divides 112 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112

Least Common Multiple of 106 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 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

Properties of LCM 106 and 112

(i) The LCM of 112 and 106 is associative

LCM of 106 and 112 = LCM of 112 and 106

Related Least Common Multiples of 106

Related Least Common Multiples of 112

Frequently Asked Questions on LCM of 106 and 112

1. What is the LCM of 106 and 112?

Answer: LCM of 106 and 112 is 5936.

2. 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.

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. How to Find the LCM of 106 and 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.