What is the Least Common Multiple of 19740 and 19755?

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 19740 and 19755 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19740 and 19755, than apply into the LCM equation.

GCF(19740,19755) = 15
LCM(19740,19755) = ( 19740 × 19755) / 15
LCM(19740,19755) = 389963700 / 15
LCM(19740,19755) = 25997580

Least Common Multiple (LCM) of 19740 and 19755 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19740 and 19755. First we will calculate the prime factors of 19740 and 19755.

Prime Factorization of 19740

Prime Factorization of 19755

Now multiplying the highest exponent prime factors to calculate the LCM of 19740 and 19755.

LCM(19740,19755) = 2² × 3² × 5¹ × 7¹ × 47¹ × 439¹
LCM(19740,19755) = 25997580