What is the Least Common Multiple of 67875 and 67890?

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 67875 and 67890 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67875 and 67890, than apply into the LCM equation.

GCF(67875,67890) = 15
LCM(67875,67890) = ( 67875 × 67890) / 15
LCM(67875,67890) = 4608033750 / 15
LCM(67875,67890) = 307202250

Least Common Multiple (LCM) of 67875 and 67890 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67875 and 67890. First we will calculate the prime factors of 67875 and 67890.

Prime Factorization of 67875

Prime Factorization of 67890

Now multiplying the highest exponent prime factors to calculate the LCM of 67875 and 67890.

LCM(67875,67890) = 3¹ × 5³ × 181¹ × 2¹ × 31¹ × 73¹
LCM(67875,67890) = 307202250