What is the Least Common Multiple of 7680 and 7684?

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 7680 and 7684 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7680 and 7684, than apply into the LCM equation.

GCF(7680,7684) = 4
LCM(7680,7684) = ( 7680 × 7684) / 4
LCM(7680,7684) = 59013120 / 4
LCM(7680,7684) = 14753280

Least Common Multiple (LCM) of 7680 and 7684 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7680 and 7684. First we will calculate the prime factors of 7680 and 7684.

Prime Factorization of 7680

Prime Factorization of 7684

Now multiplying the highest exponent prime factors to calculate the LCM of 7680 and 7684.

LCM(7680,7684) = 2⁹ × 3¹ × 5¹ × 17¹ × 113¹
LCM(7680,7684) = 14753280