What is the Least Common Multiple of 75200 and 75206?

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 75200 and 75206 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75200 and 75206, than apply into the LCM equation.

GCF(75200,75206) = 2
LCM(75200,75206) = ( 75200 × 75206) / 2
LCM(75200,75206) = 5655491200 / 2
LCM(75200,75206) = 2827745600

Least Common Multiple (LCM) of 75200 and 75206 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75200 and 75206. First we will calculate the prime factors of 75200 and 75206.

Prime Factorization of 75200

Prime Factorization of 75206

Now multiplying the highest exponent prime factors to calculate the LCM of 75200 and 75206.

LCM(75200,75206) = 2⁶ × 5² × 47¹ × 31¹ × 1213¹
LCM(75200,75206) = 2827745600