What is the Least Common Multiple of 16740 and 16749?

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 16740 and 16749 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16740 and 16749, than apply into the LCM equation.

GCF(16740,16749) = 9
LCM(16740,16749) = ( 16740 × 16749) / 9
LCM(16740,16749) = 280378260 / 9
LCM(16740,16749) = 31153140

Least Common Multiple (LCM) of 16740 and 16749 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16740 and 16749. First we will calculate the prime factors of 16740 and 16749.

Prime Factorization of 16740

Prime Factorization of 16749

Now multiplying the highest exponent prime factors to calculate the LCM of 16740 and 16749.

LCM(16740,16749) = 2² × 3³ × 5¹ × 31¹ × 1861¹
LCM(16740,16749) = 31153140