What is the Least Common Multiple of 67920 and 67935?

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 67920 and 67935 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67920 and 67935, than apply into the LCM equation.

GCF(67920,67935) = 15
LCM(67920,67935) = ( 67920 × 67935) / 15
LCM(67920,67935) = 4614145200 / 15
LCM(67920,67935) = 307609680

Least Common Multiple (LCM) of 67920 and 67935 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67920 and 67935. First we will calculate the prime factors of 67920 and 67935.

Prime Factorization of 67920

Prime Factorization of 67935

Now multiplying the highest exponent prime factors to calculate the LCM of 67920 and 67935.

LCM(67920,67935) = 2⁴ × 3¹ × 5¹ × 283¹ × 7¹ × 647¹
LCM(67920,67935) = 307609680