What is the Least Common Multiple of 69120 and 69135?

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 69120 and 69135 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69120 and 69135, than apply into the LCM equation.

GCF(69120,69135) = 15
LCM(69120,69135) = ( 69120 × 69135) / 15
LCM(69120,69135) = 4778611200 / 15
LCM(69120,69135) = 318574080

Least Common Multiple (LCM) of 69120 and 69135 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69120 and 69135. First we will calculate the prime factors of 69120 and 69135.

Prime Factorization of 69120

Prime Factorization of 69135

Now multiplying the highest exponent prime factors to calculate the LCM of 69120 and 69135.

LCM(69120,69135) = 2⁹ × 3³ × 5¹ × 11¹ × 419¹
LCM(69120,69135) = 318574080