What is the Least Common Multiple of 5400 and 5420?

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 5400 and 5420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5400 and 5420, than apply into the LCM equation.

GCF(5400,5420) = 20
LCM(5400,5420) = ( 5400 × 5420) / 20
LCM(5400,5420) = 29268000 / 20
LCM(5400,5420) = 1463400

Least Common Multiple (LCM) of 5400 and 5420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5400 and 5420. First we will calculate the prime factors of 5400 and 5420.

Prime Factorization of 5400

Prime Factorization of 5420

Now multiplying the highest exponent prime factors to calculate the LCM of 5400 and 5420.

LCM(5400,5420) = 2³ × 3³ × 5² × 271¹
LCM(5400,5420) = 1463400