What is the Least Common Multiple of 76704 and 76714?

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 76704 and 76714 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76704 and 76714, than apply into the LCM equation.

GCF(76704,76714) = 2
LCM(76704,76714) = ( 76704 × 76714) / 2
LCM(76704,76714) = 5884270656 / 2
LCM(76704,76714) = 2942135328

Least Common Multiple (LCM) of 76704 and 76714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76704 and 76714. First we will calculate the prime factors of 76704 and 76714.

Prime Factorization of 76704

Prime Factorization of 76714

Now multiplying the highest exponent prime factors to calculate the LCM of 76704 and 76714.

LCM(76704,76714) = 2⁵ × 3¹ × 17¹ × 47¹ × 11² × 317¹
LCM(76704,76714) = 2942135328