What is the Least Common Multiple of 65300 and 65314?

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 65300 and 65314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65300 and 65314, than apply into the LCM equation.

GCF(65300,65314) = 2
LCM(65300,65314) = ( 65300 × 65314) / 2
LCM(65300,65314) = 4265004200 / 2
LCM(65300,65314) = 2132502100

Least Common Multiple (LCM) of 65300 and 65314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65300 and 65314. First we will calculate the prime factors of 65300 and 65314.

Prime Factorization of 65300

Prime Factorization of 65314

Now multiplying the highest exponent prime factors to calculate the LCM of 65300 and 65314.

LCM(65300,65314) = 2² × 5² × 653¹ × 17² × 113¹
LCM(65300,65314) = 2132502100