Least Common Multiple of 105 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 105 and 112 the smallest integer that is 1680 that is divisible by both numbers.

Least Common Multiple (LCM) of 105 and 112 is 1680.

LCM(105,112) = 1680

LCM of 105 and 112

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

LCM of:
and

Least Common Multiple of 105 and 112

LCM of 105 and 112 is 1680

Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 112. First we will calculate the prime factors of 105 and 112.

Prime Factorization of 105


3 105
5 35
7 7
1

Prime factors of 105 are 3, 5,7. Prime factorization of 105 in exponential form is:

105 = 31×51×71

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 105 and 112.

LCM(105,112) = 24×31×51×71
LCM(105,112) = 1680

Factors of 105

List of positive integer factors of 105 that divides 105 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105

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 105 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 105 and 112, than apply into the LCM equation.

GCF(105,112) = 7
LCM(105,112) = ( 105 × 112) / 7
LCM(105,112) = 11760 / 7
LCM(105,112) = 1680

Properties of LCM 105 and 112

(i) The LCM of 112 and 105 is associative

LCM of 105 and 112 = LCM of 112 and 105

Related Least Common Multiples of 105

Related Least Common Multiples of 112

Frequently Asked Questions on LCM of 105 and 112

1. What is the LCM of 105 and 112?

Answer: LCM of 105 and 112 is 1680.

2. What are the Factors of 105?

Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.

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 105 and 112?

Answer:

Least Common Multiple of 105 and 112 = 1680

Step 1: Find the prime factorization of 105

105 = 3 x 5 x 7

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 = 1680 = 2 x 2 x 2 x 2 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 105 and 112 is 1680.