What is the Least Common Multiple of 59745 and 59760?

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 59745 and 59760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 59745 and 59760, than apply into the LCM equation.

GCF(59745,59760) = 15
LCM(59745,59760) = ( 59745 × 59760) / 15
LCM(59745,59760) = 3570361200 / 15
LCM(59745,59760) = 238024080

Least Common Multiple (LCM) of 59745 and 59760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 59745 and 59760. First we will calculate the prime factors of 59745 and 59760.

Prime Factorization of 59745

Prime Factorization of 59760

Now multiplying the highest exponent prime factors to calculate the LCM of 59745 and 59760.

LCM(59745,59760) = 3² × 5¹ × 7¹ × 569¹ × 2⁴ × 83¹
LCM(59745,59760) = 238024080