What is the Least Common Multiple of 19700 and 19712?

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 19700 and 19712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19700 and 19712, than apply into the LCM equation.

GCF(19700,19712) = 4
LCM(19700,19712) = ( 19700 × 19712) / 4
LCM(19700,19712) = 388326400 / 4
LCM(19700,19712) = 97081600

Least Common Multiple (LCM) of 19700 and 19712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19700 and 19712. First we will calculate the prime factors of 19700 and 19712.

Prime Factorization of 19700

Prime Factorization of 19712

Now multiplying the highest exponent prime factors to calculate the LCM of 19700 and 19712.

LCM(19700,19712) = 2⁸ × 5² × 197¹ × 7¹ × 11¹
LCM(19700,19712) = 97081600