What is the Least Common Multiple of 27405 and 27420?

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 27405 and 27420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27405 and 27420, than apply into the LCM equation.

GCF(27405,27420) = 15
LCM(27405,27420) = ( 27405 × 27420) / 15
LCM(27405,27420) = 751445100 / 15
LCM(27405,27420) = 50096340

Least Common Multiple (LCM) of 27405 and 27420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27405 and 27420. First we will calculate the prime factors of 27405 and 27420.

Prime Factorization of 27405

Prime Factorization of 27420

Now multiplying the highest exponent prime factors to calculate the LCM of 27405 and 27420.

LCM(27405,27420) = 3³ × 5¹ × 7¹ × 29¹ × 2² × 457¹
LCM(27405,27420) = 50096340