What is the Least Common Multiple of 5123 and 5138?

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 5123 and 5138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5123 and 5138, than apply into the LCM equation.

GCF(5123,5138) = 1
LCM(5123,5138) = ( 5123 × 5138) / 1
LCM(5123,5138) = 26321974 / 1
LCM(5123,5138) = 26321974

Least Common Multiple (LCM) of 5123 and 5138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5123 and 5138. First we will calculate the prime factors of 5123 and 5138.

Prime Factorization of 5123

Prime Factorization of 5138

Now multiplying the highest exponent prime factors to calculate the LCM of 5123 and 5138.

LCM(5123,5138) = 47¹ × 109¹ × 2¹ × 7¹ × 367¹
LCM(5123,5138) = 26321974