What is the Least Common Multiple of 5390 and 5408?

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 5390 and 5408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5390 and 5408, than apply into the LCM equation.

GCF(5390,5408) = 2
LCM(5390,5408) = ( 5390 × 5408) / 2
LCM(5390,5408) = 29149120 / 2
LCM(5390,5408) = 14574560

Least Common Multiple (LCM) of 5390 and 5408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5390 and 5408. First we will calculate the prime factors of 5390 and 5408.

Prime Factorization of 5390

Prime Factorization of 5408

Now multiplying the highest exponent prime factors to calculate the LCM of 5390 and 5408.

LCM(5390,5408) = 2⁵ × 5¹ × 7² × 11¹ × 13²
LCM(5390,5408) = 14574560