What is the Least Common Multiple of 5109 and 5124?

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 5109 and 5124 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5109 and 5124, than apply into the LCM equation.

GCF(5109,5124) = 3
LCM(5109,5124) = ( 5109 × 5124) / 3
LCM(5109,5124) = 26178516 / 3
LCM(5109,5124) = 8726172

Least Common Multiple (LCM) of 5109 and 5124 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5109 and 5124. First we will calculate the prime factors of 5109 and 5124.

Prime Factorization of 5109

Prime Factorization of 5124

Now multiplying the highest exponent prime factors to calculate the LCM of 5109 and 5124.

LCM(5109,5124) = 3¹ × 13¹ × 131¹ × 2² × 7¹ × 61¹
LCM(5109,5124) = 8726172