What is the Least Common Multiple of 70305 and 70320?

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 70305 and 70320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 70305 and 70320, than apply into the LCM equation.

GCF(70305,70320) = 15
LCM(70305,70320) = ( 70305 × 70320) / 15
LCM(70305,70320) = 4943847600 / 15
LCM(70305,70320) = 329589840

Least Common Multiple (LCM) of 70305 and 70320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 70305 and 70320. First we will calculate the prime factors of 70305 and 70320.

Prime Factorization of 70305

Prime Factorization of 70320

Now multiplying the highest exponent prime factors to calculate the LCM of 70305 and 70320.

LCM(70305,70320) = 3¹ × 5¹ × 43¹ × 109¹ × 2⁴ × 293¹
LCM(70305,70320) = 329589840