What is the Least Common Multiple of 34140 and 34160?

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 34140 and 34160 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34140 and 34160, than apply into the LCM equation.

GCF(34140,34160) = 20
LCM(34140,34160) = ( 34140 × 34160) / 20
LCM(34140,34160) = 1166222400 / 20
LCM(34140,34160) = 58311120

Least Common Multiple (LCM) of 34140 and 34160 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34140 and 34160. First we will calculate the prime factors of 34140 and 34160.

Prime Factorization of 34140

Prime Factorization of 34160

Now multiplying the highest exponent prime factors to calculate the LCM of 34140 and 34160.

LCM(34140,34160) = 2⁴ × 3¹ × 5¹ × 569¹ × 7¹ × 61¹
LCM(34140,34160) = 58311120