What is the Least Common Multiple of 1010 and 1030?

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 1010 and 1030 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1010 and 1030, than apply into the LCM equation.

GCF(1010,1030) = 10
LCM(1010,1030) = ( 1010 × 1030) / 10
LCM(1010,1030) = 1040300 / 10
LCM(1010,1030) = 104030

Least Common Multiple (LCM) of 1010 and 1030 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1010 and 1030. First we will calculate the prime factors of 1010 and 1030.

Prime Factorization of 1010

Prime Factorization of 1030

Now multiplying the highest exponent prime factors to calculate the LCM of 1010 and 1030.

LCM(1010,1030) = 2¹ × 5¹ × 101¹ × 103¹
LCM(1010,1030) = 104030