What is the Least Common Multiple of 55680 and 55690?

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 55690 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 55690, than apply into the LCM equation.

GCF(55680,55690) = 10
LCM(55680,55690) = ( 55680 × 55690) / 10
LCM(55680,55690) = 3100819200 / 10
LCM(55680,55690) = 310081920

Least Common Multiple (LCM) of 55680 and 55690 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55680 and 55690. First we will calculate the prime factors of 55680 and 55690.

Prime Factorization of 55680

Prime Factorization of 55690

Now multiplying the highest exponent prime factors to calculate the LCM of 55680 and 55690.

LCM(55680,55690) = 2⁷ × 3¹ × 5¹ × 29¹ × 5569¹
LCM(55680,55690) = 310081920