What is the Least Common Multiple of 20064 and 20075?

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 20064 and 20075 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20064 and 20075, than apply into the LCM equation.

GCF(20064,20075) = 11
LCM(20064,20075) = ( 20064 × 20075) / 11
LCM(20064,20075) = 402784800 / 11
LCM(20064,20075) = 36616800

Least Common Multiple (LCM) of 20064 and 20075 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20064 and 20075. First we will calculate the prime factors of 20064 and 20075.

Prime Factorization of 20064

Prime Factorization of 20075

Now multiplying the highest exponent prime factors to calculate the LCM of 20064 and 20075.

LCM(20064,20075) = 2⁵ × 3¹ × 11¹ × 19¹ × 5² × 73¹
LCM(20064,20075) = 36616800