What is the Least Common Multiple of 2170 and 2184?

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 2170 and 2184 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2170 and 2184, than apply into the LCM equation.

GCF(2170,2184) = 14
LCM(2170,2184) = ( 2170 × 2184) / 14
LCM(2170,2184) = 4739280 / 14
LCM(2170,2184) = 338520

Least Common Multiple (LCM) of 2170 and 2184 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2170 and 2184. First we will calculate the prime factors of 2170 and 2184.

Prime Factorization of 2170

Prime Factorization of 2184

Now multiplying the highest exponent prime factors to calculate the LCM of 2170 and 2184.

LCM(2170,2184) = 2³ × 5¹ × 7¹ × 31¹ × 3¹ × 13¹
LCM(2170,2184) = 338520