What is the Least Common Multiple of 75105 and 75123?

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 75105 and 75123 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75105 and 75123, than apply into the LCM equation.

GCF(75105,75123) = 9
LCM(75105,75123) = ( 75105 × 75123) / 9
LCM(75105,75123) = 5642112915 / 9
LCM(75105,75123) = 626901435

Least Common Multiple (LCM) of 75105 and 75123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75105 and 75123. First we will calculate the prime factors of 75105 and 75123.

Prime Factorization of 75105

Prime Factorization of 75123

Now multiplying the highest exponent prime factors to calculate the LCM of 75105 and 75123.

LCM(75105,75123) = 3² × 5¹ × 1669¹ × 17¹ × 491¹
LCM(75105,75123) = 626901435