What is the Least Common Multiple of 10200 and 10210?

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 10200 and 10210 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10200 and 10210, than apply into the LCM equation.

GCF(10200,10210) = 10
LCM(10200,10210) = ( 10200 × 10210) / 10
LCM(10200,10210) = 104142000 / 10
LCM(10200,10210) = 10414200

Least Common Multiple (LCM) of 10200 and 10210 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10200 and 10210. First we will calculate the prime factors of 10200 and 10210.

Prime Factorization of 10200

Prime Factorization of 10210

Now multiplying the highest exponent prime factors to calculate the LCM of 10200 and 10210.

LCM(10200,10210) = 2³ × 3¹ × 5² × 17¹ × 1021¹
LCM(10200,10210) = 10414200