What is the Least Common Multiple of 72345 and 72354?

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 72345 and 72354 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72345 and 72354, than apply into the LCM equation.

GCF(72345,72354) = 3
LCM(72345,72354) = ( 72345 × 72354) / 3
LCM(72345,72354) = 5234450130 / 3
LCM(72345,72354) = 1744816710

Least Common Multiple (LCM) of 72345 and 72354 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72345 and 72354. First we will calculate the prime factors of 72345 and 72354.

Prime Factorization of 72345

Prime Factorization of 72354

Now multiplying the highest exponent prime factors to calculate the LCM of 72345 and 72354.

LCM(72345,72354) = 3¹ × 5¹ × 7¹ × 13¹ × 53¹ × 2¹ × 31¹ × 389¹
LCM(72345,72354) = 1744816710