What is the Least Common Multiple of 9702 and 9712?

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 9702 and 9712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9702 and 9712, than apply into the LCM equation.

GCF(9702,9712) = 2
LCM(9702,9712) = ( 9702 × 9712) / 2
LCM(9702,9712) = 94225824 / 2
LCM(9702,9712) = 47112912

Least Common Multiple (LCM) of 9702 and 9712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9702 and 9712. First we will calculate the prime factors of 9702 and 9712.

Prime Factorization of 9702

Prime Factorization of 9712

Now multiplying the highest exponent prime factors to calculate the LCM of 9702 and 9712.

LCM(9702,9712) = 2⁴ × 3² × 7² × 11¹ × 607¹
LCM(9702,9712) = 47112912