What is the Least Common Multiple of 39704 and 39712?

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 39704 and 39712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39704 and 39712, than apply into the LCM equation.

GCF(39704,39712) = 8
LCM(39704,39712) = ( 39704 × 39712) / 8
LCM(39704,39712) = 1576725248 / 8
LCM(39704,39712) = 197090656

Least Common Multiple (LCM) of 39704 and 39712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39704 and 39712. First we will calculate the prime factors of 39704 and 39712.

Prime Factorization of 39704

Prime Factorization of 39712

Now multiplying the highest exponent prime factors to calculate the LCM of 39704 and 39712.

LCM(39704,39712) = 2⁵ × 7¹ × 709¹ × 17¹ × 73¹
LCM(39704,39712) = 197090656