What is the Least Common Multiple of 75702 and 75712?

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 75702 and 75712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75702 and 75712, than apply into the LCM equation.

GCF(75702,75712) = 2
LCM(75702,75712) = ( 75702 × 75712) / 2
LCM(75702,75712) = 5731549824 / 2
LCM(75702,75712) = 2865774912

Least Common Multiple (LCM) of 75702 and 75712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75702 and 75712. First we will calculate the prime factors of 75702 and 75712.

Prime Factorization of 75702

Prime Factorization of 75712

Now multiplying the highest exponent prime factors to calculate the LCM of 75702 and 75712.

LCM(75702,75712) = 2⁶ × 3¹ × 11¹ × 31¹ × 37¹ × 7¹ × 13²
LCM(75702,75712) = 2865774912