What is the Least Common Multiple of 3120 and 3140?

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 3120 and 3140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3120 and 3140, than apply into the LCM equation.

GCF(3120,3140) = 20
LCM(3120,3140) = ( 3120 × 3140) / 20
LCM(3120,3140) = 9796800 / 20
LCM(3120,3140) = 489840

Least Common Multiple (LCM) of 3120 and 3140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3120 and 3140. First we will calculate the prime factors of 3120 and 3140.

Prime Factorization of 3120

Prime Factorization of 3140

Now multiplying the highest exponent prime factors to calculate the LCM of 3120 and 3140.

LCM(3120,3140) = 2⁴ × 3¹ × 5¹ × 13¹ × 157¹
LCM(3120,3140) = 489840