What is the Least Common Multiple of 74400 and 74412?

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 74400 and 74412 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 74400 and 74412, than apply into the LCM equation.

GCF(74400,74412) = 12
LCM(74400,74412) = ( 74400 × 74412) / 12
LCM(74400,74412) = 5536252800 / 12
LCM(74400,74412) = 461354400

Least Common Multiple (LCM) of 74400 and 74412 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 74400 and 74412. First we will calculate the prime factors of 74400 and 74412.

Prime Factorization of 74400

Prime Factorization of 74412

Now multiplying the highest exponent prime factors to calculate the LCM of 74400 and 74412.

LCM(74400,74412) = 2⁵ × 3³ × 5² × 31¹ × 13¹ × 53¹
LCM(74400,74412) = 461354400