What is the Least Common Multiple of 15105 and 15123?

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 of 15105 and 15123 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15105 and 15123, than apply into the LCM equation.

GCF(15105,15123) = 3
LCM(15105,15123) = ( 15105 × 15123) / 3
LCM(15105,15123) = 228432915 / 3
LCM(15105,15123) = 76144305

Least Common Multiple (LCM) of 15105 and 15123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15105 and 15123. First we will calculate the prime factors of 15105 and 15123.

Prime Factorization of 15105

Prime Factorization of 15123

Now multiplying the highest exponent prime factors to calculate the LCM of 15105 and 15123.

LCM(15105,15123) = 3¹ × 5¹ × 19¹ × 53¹ × 71²
LCM(15105,15123) = 76144305