What is the Least Common Multiple of 57408 and 57420?

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 57408 and 57420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57408 and 57420, than apply into the LCM equation.

GCF(57408,57420) = 12
LCM(57408,57420) = ( 57408 × 57420) / 12
LCM(57408,57420) = 3296367360 / 12
LCM(57408,57420) = 274697280

Least Common Multiple (LCM) of 57408 and 57420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57408 and 57420. First we will calculate the prime factors of 57408 and 57420.

Prime Factorization of 57408

Prime Factorization of 57420

Now multiplying the highest exponent prime factors to calculate the LCM of 57408 and 57420.

LCM(57408,57420) = 2⁶ × 3² × 13¹ × 23¹ × 5¹ × 11¹ × 29¹
LCM(57408,57420) = 274697280