What is the Least Common Multiple of 84075 and 84084?

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 84075 and 84084 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84075 and 84084, than apply into the LCM equation.

GCF(84075,84084) = 3
LCM(84075,84084) = ( 84075 × 84084) / 3
LCM(84075,84084) = 7069362300 / 3
LCM(84075,84084) = 2356454100

Least Common Multiple (LCM) of 84075 and 84084 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 84075 and 84084. First we will calculate the prime factors of 84075 and 84084.

Prime Factorization of 84075

Prime Factorization of 84084

Now multiplying the highest exponent prime factors to calculate the LCM of 84075 and 84084.

LCM(84075,84084) = 3¹ × 5² × 19¹ × 59¹ × 2² × 7² × 11¹ × 13¹
LCM(84075,84084) = 2356454100