Least Common Multiple of 112 and 120

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 112 and 120 the smallest integer that is 1680 that is divisible by both numbers.

Least Common Multiple (LCM) of 112 and 120 is 1680.

LCM(112,120) = 1680

LCM of 112 and 120

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

LCM of:
and

Least Common Multiple of 112 and 120

LCM of 112 and 120 is 1680

Least common multiple can be found by multiplying the highest exponent prime factors of 112 and 120. First we will calculate the prime factors of 112 and 120.

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

Prime Factorization of 120


2 120
2 60
2 30
3 15
5 5
1

Prime factors of 120 are 2, 3,5. Prime factorization of 120 in exponential form is:

120 = 23×31×51

Now multiplying the highest exponent prime factors to calculate the LCM of 112 and 120.

LCM(112,120) = 24×31×51×71
LCM(112,120) = 1680

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

Factors of 120

List of positive integer factors of 120 that divides 120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Least Common Multiple of 112 and 120 with GCF Formula

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

Properties of LCM 112 and 120

(i) The LCM of 120 and 112 is associative

LCM of 112 and 120 = LCM of 120 and 112

Related Least Common Multiples of 112

Related Least Common Multiples of 120

Frequently Asked Questions on LCM of 112 and 120

1. What is the LCM of 112 and 120?

Answer: LCM of 112 and 120 is 1680.

2. 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.

3. 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.

4. How to Find the LCM of 112 and 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.