What is the Least Common Multiple of 19740 and 19749?

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 19749 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 19749, than apply into the LCM equation.

GCF(19740,19749) = 3
LCM(19740,19749) = ( 19740 × 19749) / 3
LCM(19740,19749) = 389845260 / 3
LCM(19740,19749) = 129948420

Least Common Multiple (LCM) of 19740 and 19749 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19740 and 19749. First we will calculate the prime factors of 19740 and 19749.

Prime Factorization of 19740

Prime Factorization of 19749

Now multiplying the highest exponent prime factors to calculate the LCM of 19740 and 19749.

LCM(19740,19749) = 2² × 3¹ × 5¹ × 7¹ × 47¹ × 29¹ × 227¹
LCM(19740,19749) = 129948420