What is the Least Common Multiple of 30688 and 30702?

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 30688 and 30702 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30688 and 30702, than apply into the LCM equation.

GCF(30688,30702) = 14
LCM(30688,30702) = ( 30688 × 30702) / 14
LCM(30688,30702) = 942182976 / 14
LCM(30688,30702) = 67298784

Least Common Multiple (LCM) of 30688 and 30702 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30688 and 30702. First we will calculate the prime factors of 30688 and 30702.

Prime Factorization of 30688

Prime Factorization of 30702

Now multiplying the highest exponent prime factors to calculate the LCM of 30688 and 30702.

LCM(30688,30702) = 2⁵ × 7¹ × 137¹ × 3¹ × 17¹ × 43¹
LCM(30688,30702) = 67298784