What is the Least Common Multiple of 78420 and 78432?

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 78420 and 78432 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78420 and 78432, than apply into the LCM equation.

GCF(78420,78432) = 12
LCM(78420,78432) = ( 78420 × 78432) / 12
LCM(78420,78432) = 6150637440 / 12
LCM(78420,78432) = 512553120

Least Common Multiple (LCM) of 78420 and 78432 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78420 and 78432. First we will calculate the prime factors of 78420 and 78432.

Prime Factorization of 78420

Prime Factorization of 78432

Now multiplying the highest exponent prime factors to calculate the LCM of 78420 and 78432.

LCM(78420,78432) = 2⁵ × 3¹ × 5¹ × 1307¹ × 19¹ × 43¹
LCM(78420,78432) = 512553120