What is the Least Common Multiple of 17688 and 17708?

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 17688 and 17708 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17688 and 17708, than apply into the LCM equation.

GCF(17688,17708) = 4
LCM(17688,17708) = ( 17688 × 17708) / 4
LCM(17688,17708) = 313219104 / 4
LCM(17688,17708) = 78304776

Least Common Multiple (LCM) of 17688 and 17708 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17688 and 17708. First we will calculate the prime factors of 17688 and 17708.

Prime Factorization of 17688

Prime Factorization of 17708

Now multiplying the highest exponent prime factors to calculate the LCM of 17688 and 17708.

LCM(17688,17708) = 2³ × 3¹ × 11¹ × 67¹ × 19¹ × 233¹
LCM(17688,17708) = 78304776