What is the Least Common Multiple of 67800 and 67815?

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 67800 and 67815 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67800 and 67815, than apply into the LCM equation.

GCF(67800,67815) = 15
LCM(67800,67815) = ( 67800 × 67815) / 15
LCM(67800,67815) = 4597857000 / 15
LCM(67800,67815) = 306523800

Least Common Multiple (LCM) of 67800 and 67815 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67800 and 67815. First we will calculate the prime factors of 67800 and 67815.

Prime Factorization of 67800

Prime Factorization of 67815

Now multiplying the highest exponent prime factors to calculate the LCM of 67800 and 67815.

LCM(67800,67815) = 2³ × 3² × 5² × 113¹ × 11¹ × 137¹
LCM(67800,67815) = 306523800