What is the Least Common Multiple of 72000 and 72006?

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 72000 and 72006 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72000 and 72006, than apply into the LCM equation.

GCF(72000,72006) = 6
LCM(72000,72006) = ( 72000 × 72006) / 6
LCM(72000,72006) = 5184432000 / 6
LCM(72000,72006) = 864072000

Least Common Multiple (LCM) of 72000 and 72006 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72000 and 72006. First we will calculate the prime factors of 72000 and 72006.

Prime Factorization of 72000

Prime Factorization of 72006

Now multiplying the highest exponent prime factors to calculate the LCM of 72000 and 72006.

LCM(72000,72006) = 2⁶ × 3² × 5³ × 11¹ × 1091¹
LCM(72000,72006) = 864072000