What is the Least Common Multiple of 73680 and 73689?

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 73680 and 73689 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 73680 and 73689, than apply into the LCM equation.

GCF(73680,73689) = 3
LCM(73680,73689) = ( 73680 × 73689) / 3
LCM(73680,73689) = 5429405520 / 3
LCM(73680,73689) = 1809801840

Least Common Multiple (LCM) of 73680 and 73689 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 73680 and 73689. First we will calculate the prime factors of 73680 and 73689.

Prime Factorization of 73680

Prime Factorization of 73689

Now multiplying the highest exponent prime factors to calculate the LCM of 73680 and 73689.

LCM(73680,73689) = 2⁴ × 3¹ × 5¹ × 307¹ × 7¹ × 11² × 29¹
LCM(73680,73689) = 1809801840