What is the Least Common Multiple of 1700 and 1712?

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 1700 and 1712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1700 and 1712, than apply into the LCM equation.

GCF(1700,1712) = 4
LCM(1700,1712) = ( 1700 × 1712) / 4
LCM(1700,1712) = 2910400 / 4
LCM(1700,1712) = 727600

Least Common Multiple (LCM) of 1700 and 1712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1700 and 1712. First we will calculate the prime factors of 1700 and 1712.

Prime Factorization of 1700

Prime Factorization of 1712

Now multiplying the highest exponent prime factors to calculate the LCM of 1700 and 1712.

LCM(1700,1712) = 2⁴ × 5² × 17¹ × 107¹
LCM(1700,1712) = 727600