What is the Least Common Multiple of 20120 and 20140?

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 20120 and 20140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20120 and 20140, than apply into the LCM equation.

GCF(20120,20140) = 20
LCM(20120,20140) = ( 20120 × 20140) / 20
LCM(20120,20140) = 405216800 / 20
LCM(20120,20140) = 20260840

Least Common Multiple (LCM) of 20120 and 20140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20120 and 20140. First we will calculate the prime factors of 20120 and 20140.

Prime Factorization of 20120

Prime Factorization of 20140

Now multiplying the highest exponent prime factors to calculate the LCM of 20120 and 20140.

LCM(20120,20140) = 2³ × 5¹ × 503¹ × 19¹ × 53¹
LCM(20120,20140) = 20260840