What is the Least Common Multiple of 7100 and 7114?

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 7100 and 7114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7100 and 7114, than apply into the LCM equation.

GCF(7100,7114) = 2
LCM(7100,7114) = ( 7100 × 7114) / 2
LCM(7100,7114) = 50509400 / 2
LCM(7100,7114) = 25254700

Least Common Multiple (LCM) of 7100 and 7114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7100 and 7114. First we will calculate the prime factors of 7100 and 7114.

Prime Factorization of 7100

Prime Factorization of 7114

Now multiplying the highest exponent prime factors to calculate the LCM of 7100 and 7114.

LCM(7100,7114) = 2² × 5² × 71¹ × 3557¹
LCM(7100,7114) = 25254700