What is the Least Common Multiple of 19509 and 19524?

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 19509 and 19524 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19509 and 19524, than apply into the LCM equation.

GCF(19509,19524) = 3
LCM(19509,19524) = ( 19509 × 19524) / 3
LCM(19509,19524) = 380893716 / 3
LCM(19509,19524) = 126964572

Least Common Multiple (LCM) of 19509 and 19524 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19509 and 19524. First we will calculate the prime factors of 19509 and 19524.

Prime Factorization of 19509

Prime Factorization of 19524

Now multiplying the highest exponent prime factors to calculate the LCM of 19509 and 19524.

LCM(19509,19524) = 3¹ × 7¹ × 929¹ × 2² × 1627¹
LCM(19509,19524) = 126964572