What is the Least Common Multiple of 76305 and 76314?

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 76305 and 76314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76305 and 76314, than apply into the LCM equation.

GCF(76305,76314) = 3
LCM(76305,76314) = ( 76305 × 76314) / 3
LCM(76305,76314) = 5823139770 / 3
LCM(76305,76314) = 1941046590

Least Common Multiple (LCM) of 76305 and 76314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76305 and 76314. First we will calculate the prime factors of 76305 and 76314.

Prime Factorization of 76305

Prime Factorization of 76314

Now multiplying the highest exponent prime factors to calculate the LCM of 76305 and 76314.

LCM(76305,76314) = 3¹ × 5¹ × 5087¹ × 2¹ × 7¹ × 23¹ × 79¹
LCM(76305,76314) = 1941046590