What is the Least Common Multiple of 10140 and 10149?

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 10140 and 10149 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10140 and 10149, than apply into the LCM equation.

GCF(10140,10149) = 3
LCM(10140,10149) = ( 10140 × 10149) / 3
LCM(10140,10149) = 102910860 / 3
LCM(10140,10149) = 34303620

Least Common Multiple (LCM) of 10140 and 10149 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10140 and 10149. First we will calculate the prime factors of 10140 and 10149.

Prime Factorization of 10140

Prime Factorization of 10149

Now multiplying the highest exponent prime factors to calculate the LCM of 10140 and 10149.

LCM(10140,10149) = 2² × 3¹ × 5¹ × 13² × 17¹ × 199¹
LCM(10140,10149) = 34303620