What is the Least Common Multiple of 67740 and 67755?

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 67740 and 67755 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67740 and 67755, than apply into the LCM equation.

GCF(67740,67755) = 15
LCM(67740,67755) = ( 67740 × 67755) / 15
LCM(67740,67755) = 4589723700 / 15
LCM(67740,67755) = 305981580

Least Common Multiple (LCM) of 67740 and 67755 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67740 and 67755. First we will calculate the prime factors of 67740 and 67755.

Prime Factorization of 67740

Prime Factorization of 67755

Now multiplying the highest exponent prime factors to calculate the LCM of 67740 and 67755.

LCM(67740,67755) = 2² × 3¹ × 5¹ × 1129¹ × 4517¹
LCM(67740,67755) = 305981580