What is the Least Common Multiple of 10102 and 10114?

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 10102 and 10114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10102 and 10114, than apply into the LCM equation.

GCF(10102,10114) = 2
LCM(10102,10114) = ( 10102 × 10114) / 2
LCM(10102,10114) = 102171628 / 2
LCM(10102,10114) = 51085814

Least Common Multiple (LCM) of 10102 and 10114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10102 and 10114. First we will calculate the prime factors of 10102 and 10114.

Prime Factorization of 10102

Prime Factorization of 10114

Now multiplying the highest exponent prime factors to calculate the LCM of 10102 and 10114.

LCM(10102,10114) = 2¹ × 5051¹ × 13¹ × 389¹
LCM(10102,10114) = 51085814