What is the Least Common Multiple of 30670 and 30688?

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 30670 and 30688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30670 and 30688, than apply into the LCM equation.

GCF(30670,30688) = 2
LCM(30670,30688) = ( 30670 × 30688) / 2
LCM(30670,30688) = 941200960 / 2
LCM(30670,30688) = 470600480

Least Common Multiple (LCM) of 30670 and 30688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30670 and 30688. First we will calculate the prime factors of 30670 and 30688.

Prime Factorization of 30670

Prime Factorization of 30688

Now multiplying the highest exponent prime factors to calculate the LCM of 30670 and 30688.

LCM(30670,30688) = 2⁵ × 5¹ × 3067¹ × 7¹ × 137¹
LCM(30670,30688) = 470600480