# What is the Least Common Multiple of 105 and 112?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 105 and 112 is 1680.

LCM(105,112) = 1680

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## 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

## Least Common Multiple (LCM) of 105 and 112 with Primes

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

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

105 = 31 × 51 × 71

### Prime Factorization of 112

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