What is the Least Common Multiple of 54549 and 54560?

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 54549 and 54560 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54549 and 54560, than apply into the LCM equation.

GCF(54549,54560) = 11
LCM(54549,54560) = ( 54549 × 54560) / 11
LCM(54549,54560) = 2976193440 / 11
LCM(54549,54560) = 270563040

Least Common Multiple (LCM) of 54549 and 54560 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54549 and 54560. First we will calculate the prime factors of 54549 and 54560.

Prime Factorization of 54549

Prime Factorization of 54560

Now multiplying the highest exponent prime factors to calculate the LCM of 54549 and 54560.

LCM(54549,54560) = 3² × 11¹ × 19¹ × 29¹ × 2⁵ × 5¹ × 31¹
LCM(54549,54560) = 270563040