What is the Least Common Multiple of 21705 and 21714?

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 21705 and 21714 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21705 and 21714, than apply into the LCM equation.

GCF(21705,21714) = 3
LCM(21705,21714) = ( 21705 × 21714) / 3
LCM(21705,21714) = 471302370 / 3
LCM(21705,21714) = 157100790

Least Common Multiple (LCM) of 21705 and 21714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21705 and 21714. First we will calculate the prime factors of 21705 and 21714.

Prime Factorization of 21705

Prime Factorization of 21714

Now multiplying the highest exponent prime factors to calculate the LCM of 21705 and 21714.

LCM(21705,21714) = 3¹ × 5¹ × 1447¹ × 2¹ × 7¹ × 11¹ × 47¹
LCM(21705,21714) = 157100790