What is the Least Common Multiple of 21609 and 21614?

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 21609 and 21614 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21609 and 21614, than apply into the LCM equation.

GCF(21609,21614) = 1
LCM(21609,21614) = ( 21609 × 21614) / 1
LCM(21609,21614) = 467056926 / 1
LCM(21609,21614) = 467056926

Least Common Multiple (LCM) of 21609 and 21614 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21609 and 21614. First we will calculate the prime factors of 21609 and 21614.

Prime Factorization of 21609

Prime Factorization of 21614

Now multiplying the highest exponent prime factors to calculate the LCM of 21609 and 21614.

LCM(21609,21614) = 3² × 7⁴ × 2¹ × 101¹ × 107¹
LCM(21609,21614) = 467056926