# 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

## 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 = 3^{1} × 5^{1} × 7^{1}

### Prime Factorization of 112

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

112 = 2^{4} × 7^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 105 and 112**.

LCM(105,112) = 3^{1} × 5^{1} × 7^{1} × 2^{4}

LCM(105,112) = 1680

#### Related Least Common Multiples of 105

- LCM of 105 and 109
- LCM of 105 and 110
- LCM of 105 and 111
- LCM of 105 and 112
- LCM of 105 and 113
- LCM of 105 and 114
- LCM of 105 and 115
- LCM of 105 and 116
- LCM of 105 and 117
- LCM of 105 and 118
- LCM of 105 and 119
- LCM of 105 and 120
- LCM of 105 and 121
- LCM of 105 and 122
- LCM of 105 and 123
- LCM of 105 and 124
- LCM of 105 and 125

#### Related Least Common Multiples of 112

- LCM of 112 and 116
- LCM of 112 and 117
- LCM of 112 and 118
- LCM of 112 and 119
- LCM of 112 and 120
- LCM of 112 and 121
- LCM of 112 and 122
- LCM of 112 and 123
- LCM of 112 and 124
- LCM of 112 and 125
- LCM of 112 and 126
- LCM of 112 and 127
- LCM of 112 and 128
- LCM of 112 and 129
- LCM of 112 and 130
- LCM of 112 and 131
- LCM of 112 and 132