What is the Least Common Multiple of 2114 and 2129?

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 2114 and 2129 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2114 and 2129, than apply into the LCM equation.

GCF(2114,2129) = 1
LCM(2114,2129) = ( 2114 × 2129) / 1
LCM(2114,2129) = 4500706 / 1
LCM(2114,2129) = 4500706

Least Common Multiple (LCM) of 2114 and 2129 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2114 and 2129. First we will calculate the prime factors of 2114 and 2129.

Prime Factorization of 2114

Prime Factorization of 2129

Now multiplying the highest exponent prime factors to calculate the LCM of 2114 and 2129.

LCM(2114,2129) = 2¹ × 7¹ × 151¹ × 2129¹
LCM(2114,2129) = 4500706