What is the Least Common Multiple of 10120 and 10140?

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 10120 and 10140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10120 and 10140, than apply into the LCM equation.

GCF(10120,10140) = 20
LCM(10120,10140) = ( 10120 × 10140) / 20
LCM(10120,10140) = 102616800 / 20
LCM(10120,10140) = 5130840

Least Common Multiple (LCM) of 10120 and 10140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10120 and 10140. First we will calculate the prime factors of 10120 and 10140.

Prime Factorization of 10120

Prime Factorization of 10140

Now multiplying the highest exponent prime factors to calculate the LCM of 10120 and 10140.

LCM(10120,10140) = 2³ × 5¹ × 11¹ × 23¹ × 3¹ × 13²
LCM(10120,10140) = 5130840