What is the Least Common Multiple of 51600 and 51614?

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 51600 and 51614 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51600 and 51614, than apply into the LCM equation.

GCF(51600,51614) = 2
LCM(51600,51614) = ( 51600 × 51614) / 2
LCM(51600,51614) = 2663282400 / 2
LCM(51600,51614) = 1331641200

Least Common Multiple (LCM) of 51600 and 51614 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51600 and 51614. First we will calculate the prime factors of 51600 and 51614.

Prime Factorization of 51600

Prime Factorization of 51614

Now multiplying the highest exponent prime factors to calculate the LCM of 51600 and 51614.

LCM(51600,51614) = 2⁴ × 3¹ × 5² × 43¹ × 131¹ × 197¹
LCM(51600,51614) = 1331641200