What is the Least Common Multiple of 45750 and 45770?

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 45750 and 45770 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45750 and 45770, than apply into the LCM equation.

GCF(45750,45770) = 10
LCM(45750,45770) = ( 45750 × 45770) / 10
LCM(45750,45770) = 2093977500 / 10
LCM(45750,45770) = 209397750

Least Common Multiple (LCM) of 45750 and 45770 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45750 and 45770. First we will calculate the prime factors of 45750 and 45770.

Prime Factorization of 45750

Prime Factorization of 45770

Now multiplying the highest exponent prime factors to calculate the LCM of 45750 and 45770.

LCM(45750,45770) = 2¹ × 3¹ × 5³ × 61¹ × 23¹ × 199¹
LCM(45750,45770) = 209397750