What is the Least Common Multiple of 45975 and 45984?

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 45975 and 45984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45975 and 45984, than apply into the LCM equation.

GCF(45975,45984) = 3
LCM(45975,45984) = ( 45975 × 45984) / 3
LCM(45975,45984) = 2114114400 / 3
LCM(45975,45984) = 704704800

Least Common Multiple (LCM) of 45975 and 45984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45975 and 45984. First we will calculate the prime factors of 45975 and 45984.

Prime Factorization of 45975

Prime Factorization of 45984

Now multiplying the highest exponent prime factors to calculate the LCM of 45975 and 45984.

LCM(45975,45984) = 3¹ × 5² × 613¹ × 2⁵ × 479¹
LCM(45975,45984) = 704704800