What is the Least Common Multiple of 21000 and 21014?

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 21000 and 21014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21000 and 21014, than apply into the LCM equation.

GCF(21000,21014) = 14
LCM(21000,21014) = ( 21000 × 21014) / 14
LCM(21000,21014) = 441294000 / 14
LCM(21000,21014) = 31521000

Least Common Multiple (LCM) of 21000 and 21014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21000 and 21014. First we will calculate the prime factors of 21000 and 21014.

Prime Factorization of 21000

Prime Factorization of 21014

Now multiplying the highest exponent prime factors to calculate the LCM of 21000 and 21014.

LCM(21000,21014) = 2³ × 3¹ × 5³ × 7¹ × 19¹ × 79¹
LCM(21000,21014) = 31521000