What is the Least Common Multiple of 67500 and 67519?

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 67500 and 67519 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67500 and 67519, than apply into the LCM equation.

GCF(67500,67519) = 1
LCM(67500,67519) = ( 67500 × 67519) / 1
LCM(67500,67519) = 4557532500 / 1
LCM(67500,67519) = 4557532500

Least Common Multiple (LCM) of 67500 and 67519 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67500 and 67519. First we will calculate the prime factors of 67500 and 67519.

Prime Factorization of 67500

Prime Factorization of 67519

Now multiplying the highest exponent prime factors to calculate the LCM of 67500 and 67519.

LCM(67500,67519) = 2² × 3³ × 5⁴ × 251¹ × 269¹
LCM(67500,67519) = 4557532500