Least Common Multiple of 104 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 104 and 112 the smallest integer that is 1456 that is divisible by both numbers.

Least Common Multiple (LCM) of 104 and 112 is 1456.

LCM(104,112) = 1456

LCM of 104 and 112

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

LCM of:
and

Least Common Multiple of 104 and 112

LCM of 104 and 112 is 1456

Least common multiple can be found by multiplying the highest exponent prime factors of 104 and 112. First we will calculate the prime factors of 104 and 112.

Prime Factorization of 104


2 104
2 52
2 26
13 13
1

Prime factors of 104 are 2,13. Prime factorization of 104 in exponential form is:

104 = 23×131

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 104 and 112.

LCM(104,112) = 24×71×131
LCM(104,112) = 1456

Factors of 104

List of positive integer factors of 104 that divides 104 without a remainder.

1, 2, 4, 8, 13, 26, 52, 104

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 104 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 104 and 112, than apply into the LCM equation.

GCF(104,112) = 8
LCM(104,112) = ( 104 × 112) / 8
LCM(104,112) = 11648 / 8
LCM(104,112) = 1456

Properties of LCM 104 and 112

(i) The LCM of 112 and 104 is associative

LCM of 104 and 112 = LCM of 112 and 104

Related Least Common Multiples of 104

Related Least Common Multiples of 112

Frequently Asked Questions on LCM of 104 and 112

1. What is the LCM of 104 and 112?

Answer: LCM of 104 and 112 is 1456.

2. What are the Factors of 104?

Answer: Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104. There are 8 integers that are factors of 104. The greatest factor of 104 is 104.

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 104 and 112?

Answer:

Least Common Multiple of 104 and 112 = 1456

Step 1: Find the prime factorization of 104

104 = 2 x 2 x 2 x 13

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 = 1456 = 2 x 2 x 2 x 2 x 7 x 13

Step 4: Therefore, the least common multiple of 104 and 112 is 1456.