# What is the Least Common Multiple of 105 and 123?

*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 123 is **4305**.

LCM(105,123) = 4305

## Least Common Multiple of 105 and 123 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 123, than apply into the LCM equation.

GCF(105,123) = 3

LCM(105,123) = ( 105 × 123) / 3

LCM(105,123) = 12915 / 3

LCM(105,123) = 4305

## Least Common Multiple (LCM) of 105 and 123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 123. First we will calculate the **prime factors of 105 and 123**.

### 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 123

Prime factors of 123 are 3, 41. Prime factorization of **123** in exponential form is:

123 = 3^{1} × 41^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 105 and 123**.

LCM(105,123) = 3^{1} × 5^{1} × 7^{1} × 41^{1}

LCM(105,123) = 4305

#### 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
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- LCM of 105 and 119
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- 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 123

- LCM of 123 and 127
- LCM of 123 and 128
- LCM of 123 and 129
- LCM of 123 and 130
- LCM of 123 and 131
- LCM of 123 and 132
- LCM of 123 and 133
- LCM of 123 and 134
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- LCM of 123 and 138
- LCM of 123 and 139
- LCM of 123 and 140
- LCM of 123 and 141
- LCM of 123 and 142
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