What is the Least Common Multiple of 75414 and 75420?

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 75414 and 75420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75414 and 75420, than apply into the LCM equation.

GCF(75414,75420) = 6
LCM(75414,75420) = ( 75414 × 75420) / 6
LCM(75414,75420) = 5687723880 / 6
LCM(75414,75420) = 947953980

Least Common Multiple (LCM) of 75414 and 75420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75414 and 75420. First we will calculate the prime factors of 75414 and 75420.

Prime Factorization of 75414

Prime Factorization of 75420

Now multiplying the highest exponent prime factors to calculate the LCM of 75414 and 75420.

LCM(75414,75420) = 2² × 3² × 12569¹ × 5¹ × 419¹
LCM(75414,75420) = 947953980