What is the Least Common Multiple of 72400 and 72420?

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 72400 and 72420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72400 and 72420, than apply into the LCM equation.

GCF(72400,72420) = 20
LCM(72400,72420) = ( 72400 × 72420) / 20
LCM(72400,72420) = 5243208000 / 20
LCM(72400,72420) = 262160400

Least Common Multiple (LCM) of 72400 and 72420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72400 and 72420. First we will calculate the prime factors of 72400 and 72420.

Prime Factorization of 72400

Prime Factorization of 72420

Now multiplying the highest exponent prime factors to calculate the LCM of 72400 and 72420.

LCM(72400,72420) = 2⁴ × 5² × 181¹ × 3¹ × 17¹ × 71¹
LCM(72400,72420) = 262160400