What is the Least Common Multiple of 72114 and 72119?

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 72114 and 72119 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72114 and 72119, than apply into the LCM equation.

GCF(72114,72119) = 1
LCM(72114,72119) = ( 72114 × 72119) / 1
LCM(72114,72119) = 5200789566 / 1
LCM(72114,72119) = 5200789566

Least Common Multiple (LCM) of 72114 and 72119 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72114 and 72119. First we will calculate the prime factors of 72114 and 72119.

Prime Factorization of 72114

Prime Factorization of 72119

Now multiplying the highest exponent prime factors to calculate the LCM of 72114 and 72119.

LCM(72114,72119) = 2¹ × 3¹ × 7¹ × 17¹ × 101¹ × 41¹ × 1759¹
LCM(72114,72119) = 5200789566