What is the Least Common Multiple of 68500 and 68512?

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 68500 and 68512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 68500 and 68512, than apply into the LCM equation.

GCF(68500,68512) = 4
LCM(68500,68512) = ( 68500 × 68512) / 4
LCM(68500,68512) = 4693072000 / 4
LCM(68500,68512) = 1173268000

Least Common Multiple (LCM) of 68500 and 68512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 68500 and 68512. First we will calculate the prime factors of 68500 and 68512.

Prime Factorization of 68500

Prime Factorization of 68512

Now multiplying the highest exponent prime factors to calculate the LCM of 68500 and 68512.

LCM(68500,68512) = 2⁵ × 5³ × 137¹ × 2141¹
LCM(68500,68512) = 1173268000