What is the Least Common Multiple of 1548 and 1565?

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 1548 and 1565 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1548 and 1565, than apply into the LCM equation.

GCF(1548,1565) = 1
LCM(1548,1565) = ( 1548 × 1565) / 1
LCM(1548,1565) = 2422620 / 1
LCM(1548,1565) = 2422620

Least Common Multiple (LCM) of 1548 and 1565 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1548 and 1565. First we will calculate the prime factors of 1548 and 1565.

Prime Factorization of 1548

Prime Factorization of 1565

Now multiplying the highest exponent prime factors to calculate the LCM of 1548 and 1565.

LCM(1548,1565) = 2² × 3² × 43¹ × 5¹ × 313¹
LCM(1548,1565) = 2422620