What is the Least Common Multiple of 48105 and 48123?

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 48105 and 48123 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48105 and 48123, than apply into the LCM equation.

GCF(48105,48123) = 9
LCM(48105,48123) = ( 48105 × 48123) / 9
LCM(48105,48123) = 2314956915 / 9
LCM(48105,48123) = 257217435

Least Common Multiple (LCM) of 48105 and 48123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 48105 and 48123. First we will calculate the prime factors of 48105 and 48123.

Prime Factorization of 48105

Prime Factorization of 48123

Now multiplying the highest exponent prime factors to calculate the LCM of 48105 and 48123.

LCM(48105,48123) = 3² × 5¹ × 1069¹ × 5347¹
LCM(48105,48123) = 257217435