What is the Least Common Multiple of 1575 and 1588?

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 1575 and 1588 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1575 and 1588, than apply into the LCM equation.

GCF(1575,1588) = 1
LCM(1575,1588) = ( 1575 × 1588) / 1
LCM(1575,1588) = 2501100 / 1
LCM(1575,1588) = 2501100

Least Common Multiple (LCM) of 1575 and 1588 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1575 and 1588. First we will calculate the prime factors of 1575 and 1588.

Prime Factorization of 1575

Prime Factorization of 1588

Now multiplying the highest exponent prime factors to calculate the LCM of 1575 and 1588.

LCM(1575,1588) = 3² × 5² × 7¹ × 2² × 397¹
LCM(1575,1588) = 2501100