What is the Least Common Multiple of 1569 and 1575?

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 1569 and 1575 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1569 and 1575, than apply into the LCM equation.

GCF(1569,1575) = 3
LCM(1569,1575) = ( 1569 × 1575) / 3
LCM(1569,1575) = 2471175 / 3
LCM(1569,1575) = 823725

Least Common Multiple (LCM) of 1569 and 1575 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1569 and 1575. First we will calculate the prime factors of 1569 and 1575.

Prime Factorization of 1569

Prime Factorization of 1575

Now multiplying the highest exponent prime factors to calculate the LCM of 1569 and 1575.

LCM(1569,1575) = 3² × 523¹ × 5² × 7¹
LCM(1569,1575) = 823725