What is the Least Common Multiple of 71712 and 71724?

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 71712 and 71724 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71712 and 71724, than apply into the LCM equation.

GCF(71712,71724) = 12
LCM(71712,71724) = ( 71712 × 71724) / 12
LCM(71712,71724) = 5143471488 / 12
LCM(71712,71724) = 428622624

Least Common Multiple (LCM) of 71712 and 71724 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 71712 and 71724. First we will calculate the prime factors of 71712 and 71724.

Prime Factorization of 71712

Prime Factorization of 71724

Now multiplying the highest exponent prime factors to calculate the LCM of 71712 and 71724.

LCM(71712,71724) = 2⁵ × 3³ × 83¹ × 43¹ × 139¹
LCM(71712,71724) = 428622624