What is the Least Common Multiple of 30105 and 30123?

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 30105 and 30123 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30105 and 30123, than apply into the LCM equation.

GCF(30105,30123) = 9
LCM(30105,30123) = ( 30105 × 30123) / 9
LCM(30105,30123) = 906852915 / 9
LCM(30105,30123) = 100761435

Least Common Multiple (LCM) of 30105 and 30123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30105 and 30123. First we will calculate the prime factors of 30105 and 30123.

Prime Factorization of 30105

Prime Factorization of 30123

Now multiplying the highest exponent prime factors to calculate the LCM of 30105 and 30123.

LCM(30105,30123) = 3³ × 5¹ × 223¹ × 3347¹
LCM(30105,30123) = 100761435