What is the Least Common Multiple of 978 and 993?

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 978 and 993 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 978 and 993, than apply into the LCM equation.

GCF(978,993) = 3
LCM(978,993) = ( 978 × 993) / 3
LCM(978,993) = 971154 / 3
LCM(978,993) = 323718

Least Common Multiple (LCM) of 978 and 993 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 978 and 993. First we will calculate the prime factors of 978 and 993.

Prime Factorization of 978

Prime Factorization of 993

Now multiplying the highest exponent prime factors to calculate the LCM of 978 and 993.

LCM(978,993) = 2¹ × 3¹ × 163¹ × 331¹
LCM(978,993) = 323718