What is the Least Common Multiple of 69108 and 69120?

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 69108 and 69120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69108 and 69120, than apply into the LCM equation.

GCF(69108,69120) = 12
LCM(69108,69120) = ( 69108 × 69120) / 12
LCM(69108,69120) = 4776744960 / 12
LCM(69108,69120) = 398062080

Least Common Multiple (LCM) of 69108 and 69120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69108 and 69120. First we will calculate the prime factors of 69108 and 69120.

Prime Factorization of 69108

Prime Factorization of 69120

Now multiplying the highest exponent prime factors to calculate the LCM of 69108 and 69120.

LCM(69108,69120) = 2⁹ × 3³ × 13¹ × 443¹ × 5¹
LCM(69108,69120) = 398062080