# 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

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## 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 = 31 × 51 × 71

### Prime Factorization of 123

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

123 = 31 × 411

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

LCM(105,123) = 31 × 51 × 71 × 411
LCM(105,123) = 4305