What is the Least Common Multiple of 21509 and 21522?

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 21509 and 21522 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21509 and 21522, than apply into the LCM equation.

GCF(21509,21522) = 1
LCM(21509,21522) = ( 21509 × 21522) / 1
LCM(21509,21522) = 462916698 / 1
LCM(21509,21522) = 462916698

Least Common Multiple (LCM) of 21509 and 21522 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21509 and 21522. First we will calculate the prime factors of 21509 and 21522.

Prime Factorization of 21509

Prime Factorization of 21522

Now multiplying the highest exponent prime factors to calculate the LCM of 21509 and 21522.

LCM(21509,21522) = 137¹ × 157¹ × 2¹ × 3¹ × 17¹ × 211¹
LCM(21509,21522) = 462916698