What is the Least Common Multiple of 78000 and 78006?

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 78000 and 78006 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78000 and 78006, than apply into the LCM equation.

GCF(78000,78006) = 6
LCM(78000,78006) = ( 78000 × 78006) / 6
LCM(78000,78006) = 6084468000 / 6
LCM(78000,78006) = 1014078000

Least Common Multiple (LCM) of 78000 and 78006 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78000 and 78006. First we will calculate the prime factors of 78000 and 78006.

Prime Factorization of 78000

Prime Factorization of 78006

Now multiplying the highest exponent prime factors to calculate the LCM of 78000 and 78006.

LCM(78000,78006) = 2⁴ × 3¹ × 5³ × 13¹ × 13001¹
LCM(78000,78006) = 1014078000