What is the Least Common Multiple of 74380 and 74400?

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 74380 and 74400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 74380 and 74400, than apply into the LCM equation.

GCF(74380,74400) = 20
LCM(74380,74400) = ( 74380 × 74400) / 20
LCM(74380,74400) = 5533872000 / 20
LCM(74380,74400) = 276693600

Least Common Multiple (LCM) of 74380 and 74400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 74380 and 74400. First we will calculate the prime factors of 74380 and 74400.

Prime Factorization of 74380

Prime Factorization of 74400

Now multiplying the highest exponent prime factors to calculate the LCM of 74380 and 74400.

LCM(74380,74400) = 2⁵ × 5² × 3719¹ × 3¹ × 31¹
LCM(74380,74400) = 276693600