What is the Least Common Multiple of 55680 and 55685?

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 55685 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 55685, than apply into the LCM equation.

GCF(55680,55685) = 5
LCM(55680,55685) = ( 55680 × 55685) / 5
LCM(55680,55685) = 3100540800 / 5
LCM(55680,55685) = 620108160

Least Common Multiple (LCM) of 55680 and 55685 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55680 and 55685. First we will calculate the prime factors of 55680 and 55685.

Prime Factorization of 55680

Prime Factorization of 55685

Now multiplying the highest exponent prime factors to calculate the LCM of 55680 and 55685.

LCM(55680,55685) = 2⁷ × 3¹ × 5¹ × 29¹ × 7¹ × 37¹ × 43¹
LCM(55680,55685) = 620108160