What is the Least Common Multiple of 30678 and 30690?

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 30678 and 30690 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30678 and 30690, than apply into the LCM equation.

GCF(30678,30690) = 6
LCM(30678,30690) = ( 30678 × 30690) / 6
LCM(30678,30690) = 941507820 / 6
LCM(30678,30690) = 156917970

Least Common Multiple (LCM) of 30678 and 30690 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30678 and 30690. First we will calculate the prime factors of 30678 and 30690.

Prime Factorization of 30678

Prime Factorization of 30690

Now multiplying the highest exponent prime factors to calculate the LCM of 30678 and 30690.

LCM(30678,30690) = 2¹ × 3² × 5113¹ × 5¹ × 11¹ × 31¹
LCM(30678,30690) = 156917970