What is the Least Common Multiple of 51684 and 51688?

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 51684 and 51688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51684 and 51688, than apply into the LCM equation.

GCF(51684,51688) = 4
LCM(51684,51688) = ( 51684 × 51688) / 4
LCM(51684,51688) = 2671442592 / 4
LCM(51684,51688) = 667860648

Least Common Multiple (LCM) of 51684 and 51688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51684 and 51688. First we will calculate the prime factors of 51684 and 51688.

Prime Factorization of 51684

Prime Factorization of 51688

Now multiplying the highest exponent prime factors to calculate the LCM of 51684 and 51688.

LCM(51684,51688) = 2³ × 3¹ × 59¹ × 73¹ × 7¹ × 13¹ × 71¹
LCM(51684,51688) = 667860648