What is the Least Common Multiple of 71990 and 72000?

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 71990 and 72000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71990 and 72000, than apply into the LCM equation.

GCF(71990,72000) = 10
LCM(71990,72000) = ( 71990 × 72000) / 10
LCM(71990,72000) = 5183280000 / 10
LCM(71990,72000) = 518328000

Least Common Multiple (LCM) of 71990 and 72000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 71990 and 72000. First we will calculate the prime factors of 71990 and 72000.

Prime Factorization of 71990

Prime Factorization of 72000

Now multiplying the highest exponent prime factors to calculate the LCM of 71990 and 72000.

LCM(71990,72000) = 2⁶ × 5³ × 23¹ × 313¹ × 3²
LCM(71990,72000) = 518328000