What is the Least Common Multiple of 5300 and 5314?

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 5300 and 5314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5300 and 5314, than apply into the LCM equation.

GCF(5300,5314) = 2
LCM(5300,5314) = ( 5300 × 5314) / 2
LCM(5300,5314) = 28164200 / 2
LCM(5300,5314) = 14082100

Least Common Multiple (LCM) of 5300 and 5314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5300 and 5314. First we will calculate the prime factors of 5300 and 5314.

Prime Factorization of 5300

Prime Factorization of 5314

Now multiplying the highest exponent prime factors to calculate the LCM of 5300 and 5314.

LCM(5300,5314) = 2² × 5² × 53¹ × 2657¹
LCM(5300,5314) = 14082100