What is the Least Common Multiple of 55680 and 55688?

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 55688 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 55688, than apply into the LCM equation.

GCF(55680,55688) = 8
LCM(55680,55688) = ( 55680 × 55688) / 8
LCM(55680,55688) = 3100707840 / 8
LCM(55680,55688) = 387588480

Least Common Multiple (LCM) of 55680 and 55688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55680 and 55688. First we will calculate the prime factors of 55680 and 55688.

Prime Factorization of 55680

Prime Factorization of 55688

Now multiplying the highest exponent prime factors to calculate the LCM of 55680 and 55688.

LCM(55680,55688) = 2⁷ × 3¹ × 5¹ × 29¹ × 6961¹
LCM(55680,55688) = 387588480