What is the Least Common Multiple of 90105 and 90123?

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 90105 and 90123 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90105 and 90123, than apply into the LCM equation.

GCF(90105,90123) = 3
LCM(90105,90123) = ( 90105 × 90123) / 3
LCM(90105,90123) = 8120532915 / 3
LCM(90105,90123) = 2706844305

Least Common Multiple (LCM) of 90105 and 90123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90105 and 90123. First we will calculate the prime factors of 90105 and 90123.

Prime Factorization of 90105

Prime Factorization of 90123

Now multiplying the highest exponent prime factors to calculate the LCM of 90105 and 90123.

LCM(90105,90123) = 3¹ × 5¹ × 6007¹ × 11¹ × 2731¹
LCM(90105,90123) = 2706844305