What is the Least Common Multiple of 70500 and 70512?

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 70500 and 70512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 70500 and 70512, than apply into the LCM equation.

GCF(70500,70512) = 12
LCM(70500,70512) = ( 70500 × 70512) / 12
LCM(70500,70512) = 4971096000 / 12
LCM(70500,70512) = 414258000

Least Common Multiple (LCM) of 70500 and 70512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 70500 and 70512. First we will calculate the prime factors of 70500 and 70512.

Prime Factorization of 70500

Prime Factorization of 70512

Now multiplying the highest exponent prime factors to calculate the LCM of 70500 and 70512.

LCM(70500,70512) = 2⁴ × 3¹ × 5³ × 47¹ × 13¹ × 113¹
LCM(70500,70512) = 414258000