What is the Least Common Multiple of 975 and 984?

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 975 and 984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 975 and 984, than apply into the LCM equation.

GCF(975,984) = 3
LCM(975,984) = ( 975 × 984) / 3
LCM(975,984) = 959400 / 3
LCM(975,984) = 319800

Least Common Multiple (LCM) of 975 and 984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 975 and 984. First we will calculate the prime factors of 975 and 984.

Prime Factorization of 975

Prime Factorization of 984

Now multiplying the highest exponent prime factors to calculate the LCM of 975 and 984.

LCM(975,984) = 3¹ × 5² × 13¹ × 2³ × 41¹
LCM(975,984) = 319800