What is the Least Common Multiple of 43680 and 43689?

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 43680 and 43689 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 43680 and 43689, than apply into the LCM equation.

GCF(43680,43689) = 3
LCM(43680,43689) = ( 43680 × 43689) / 3
LCM(43680,43689) = 1908335520 / 3
LCM(43680,43689) = 636111840

Least Common Multiple (LCM) of 43680 and 43689 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 43680 and 43689. First we will calculate the prime factors of 43680 and 43689.

Prime Factorization of 43680

Prime Factorization of 43689

Now multiplying the highest exponent prime factors to calculate the LCM of 43680 and 43689.

LCM(43680,43689) = 2⁵ × 3¹ × 5¹ × 7¹ × 13¹ × 14563¹
LCM(43680,43689) = 636111840