What is the Least Common Multiple of 27680 and 27690?

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 27680 and 27690 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27680 and 27690, than apply into the LCM equation.

GCF(27680,27690) = 10
LCM(27680,27690) = ( 27680 × 27690) / 10
LCM(27680,27690) = 766459200 / 10
LCM(27680,27690) = 76645920

Least Common Multiple (LCM) of 27680 and 27690 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27680 and 27690. First we will calculate the prime factors of 27680 and 27690.

Prime Factorization of 27680

Prime Factorization of 27690

Now multiplying the highest exponent prime factors to calculate the LCM of 27680 and 27690.

LCM(27680,27690) = 2⁵ × 5¹ × 173¹ × 3¹ × 13¹ × 71¹
LCM(27680,27690) = 76645920