What is the Least Common Multiple of 33405 and 33420?

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 33405 and 33420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33405 and 33420, than apply into the LCM equation.

GCF(33405,33420) = 15
LCM(33405,33420) = ( 33405 × 33420) / 15
LCM(33405,33420) = 1116395100 / 15
LCM(33405,33420) = 74426340

Least Common Multiple (LCM) of 33405 and 33420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33405 and 33420. First we will calculate the prime factors of 33405 and 33420.

Prime Factorization of 33405

Prime Factorization of 33420

Now multiplying the highest exponent prime factors to calculate the LCM of 33405 and 33420.

LCM(33405,33420) = 3¹ × 5¹ × 17¹ × 131¹ × 2² × 557¹
LCM(33405,33420) = 74426340