What is the Least Common Multiple of 20986 and 21000?

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 20986 and 21000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20986 and 21000, than apply into the LCM equation.

GCF(20986,21000) = 14
LCM(20986,21000) = ( 20986 × 21000) / 14
LCM(20986,21000) = 440706000 / 14
LCM(20986,21000) = 31479000

Least Common Multiple (LCM) of 20986 and 21000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20986 and 21000. First we will calculate the prime factors of 20986 and 21000.

Prime Factorization of 20986

Prime Factorization of 21000

Now multiplying the highest exponent prime factors to calculate the LCM of 20986 and 21000.

LCM(20986,21000) = 2³ × 7¹ × 1499¹ × 3¹ × 5³
LCM(20986,21000) = 31479000