# What is the Least Common Multiple of 102 and 120?

*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 102 and 120 is **2040**.

LCM(102,120) = 2040

## Least Common Multiple of 102 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 102 and 120, than apply into the LCM equation.

GCF(102,120) = 6

LCM(102,120) = ( 102 × 120) / 6

LCM(102,120) = 12240 / 6

LCM(102,120) = 2040

## Least Common Multiple (LCM) of 102 and 120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 102 and 120. First we will calculate the **prime factors of 102 and 120**.

### Prime Factorization of 102

Prime factors of 102 are 2, 3, 17. Prime factorization of **102** in exponential form is:

102 = 2^{1} × 3^{1} × 17^{1}

### Prime Factorization of 120

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

120 = 2^{3} × 3^{1} × 5^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 102 and 120**.

LCM(102,120) = 2^{3} × 3^{1} × 17^{1} × 5^{1}

LCM(102,120) = 2040

#### Related Least Common Multiples of 102

- LCM of 102 and 106
- LCM of 102 and 107
- LCM of 102 and 108
- LCM of 102 and 109
- LCM of 102 and 110
- LCM of 102 and 111
- LCM of 102 and 112
- LCM of 102 and 113
- LCM of 102 and 114
- LCM of 102 and 115
- LCM of 102 and 116
- LCM of 102 and 117
- LCM of 102 and 118
- LCM of 102 and 119
- LCM of 102 and 120
- LCM of 102 and 121
- LCM of 102 and 122

#### Related Least Common Multiples of 120

- LCM of 120 and 124
- LCM of 120 and 125
- LCM of 120 and 126
- LCM of 120 and 127
- LCM of 120 and 128
- LCM of 120 and 129
- LCM of 120 and 130
- LCM of 120 and 131
- LCM of 120 and 132
- LCM of 120 and 133
- LCM of 120 and 134
- LCM of 120 and 135
- LCM of 120 and 136
- LCM of 120 and 137
- LCM of 120 and 138
- LCM of 120 and 139
- LCM of 120 and 140