What is the Least Common Multiple of 8214 and 8225?

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 8214 and 8225 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8214 and 8225, than apply into the LCM equation.

GCF(8214,8225) = 1
LCM(8214,8225) = ( 8214 × 8225) / 1
LCM(8214,8225) = 67560150 / 1
LCM(8214,8225) = 67560150

Least Common Multiple (LCM) of 8214 and 8225 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8214 and 8225. First we will calculate the prime factors of 8214 and 8225.

Prime Factorization of 8214

Prime Factorization of 8225

Now multiplying the highest exponent prime factors to calculate the LCM of 8214 and 8225.

LCM(8214,8225) = 2¹ × 3¹ × 37² × 5² × 7¹ × 47¹
LCM(8214,8225) = 67560150