What is the Least Common Multiple of 67584 and 67590?

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 67584 and 67590 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67584 and 67590, than apply into the LCM equation.

GCF(67584,67590) = 6
LCM(67584,67590) = ( 67584 × 67590) / 6
LCM(67584,67590) = 4568002560 / 6
LCM(67584,67590) = 761333760

Least Common Multiple (LCM) of 67584 and 67590 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67584 and 67590. First we will calculate the prime factors of 67584 and 67590.

Prime Factorization of 67584

Prime Factorization of 67590

Now multiplying the highest exponent prime factors to calculate the LCM of 67584 and 67590.

LCM(67584,67590) = 2¹¹ × 3² × 11¹ × 5¹ × 751¹
LCM(67584,67590) = 761333760