What is the Least Common Multiple of 10005 and 10023?

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 10005 and 10023 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10005 and 10023, than apply into the LCM equation.

GCF(10005,10023) = 3
LCM(10005,10023) = ( 10005 × 10023) / 3
LCM(10005,10023) = 100280115 / 3
LCM(10005,10023) = 33426705

Least Common Multiple (LCM) of 10005 and 10023 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10005 and 10023. First we will calculate the prime factors of 10005 and 10023.

Prime Factorization of 10005

Prime Factorization of 10023

Now multiplying the highest exponent prime factors to calculate the LCM of 10005 and 10023.

LCM(10005,10023) = 3¹ × 5¹ × 23¹ × 29¹ × 13¹ × 257¹
LCM(10005,10023) = 33426705