What is the Least Common Multiple of 19749 and 19760?

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 19749 and 19760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19749 and 19760, than apply into the LCM equation.

GCF(19749,19760) = 1
LCM(19749,19760) = ( 19749 × 19760) / 1
LCM(19749,19760) = 390240240 / 1
LCM(19749,19760) = 390240240

Least Common Multiple (LCM) of 19749 and 19760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19749 and 19760. First we will calculate the prime factors of 19749 and 19760.

Prime Factorization of 19749

Prime Factorization of 19760

Now multiplying the highest exponent prime factors to calculate the LCM of 19749 and 19760.

LCM(19749,19760) = 3¹ × 29¹ × 227¹ × 2⁴ × 5¹ × 13¹ × 19¹
LCM(19749,19760) = 390240240