What is the Least Common Multiple of 30705 and 30714?

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 30705 and 30714 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30705 and 30714, than apply into the LCM equation.

GCF(30705,30714) = 3
LCM(30705,30714) = ( 30705 × 30714) / 3
LCM(30705,30714) = 943073370 / 3
LCM(30705,30714) = 314357790

Least Common Multiple (LCM) of 30705 and 30714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30705 and 30714. First we will calculate the prime factors of 30705 and 30714.

Prime Factorization of 30705

Prime Factorization of 30714

Now multiplying the highest exponent prime factors to calculate the LCM of 30705 and 30714.

LCM(30705,30714) = 3¹ × 5¹ × 23¹ × 89¹ × 2¹ × 5119¹
LCM(30705,30714) = 314357790