What is the Least Common Multiple of 55680 and 55689?

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 55680 and 55689 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 55680 and 55689, than apply into the LCM equation.

GCF(55680,55689) = 3
LCM(55680,55689) = ( 55680 × 55689) / 3
LCM(55680,55689) = 3100763520 / 3
LCM(55680,55689) = 1033587840

Least Common Multiple (LCM) of 55680 and 55689 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55680 and 55689. First we will calculate the prime factors of 55680 and 55689.

Prime Factorization of 55680

Prime Factorization of 55689

Now multiplying the highest exponent prime factors to calculate the LCM of 55680 and 55689.

LCM(55680,55689) = 2⁷ × 3¹ × 5¹ × 29¹ × 19¹ × 977¹
LCM(55680,55689) = 1033587840