What is the Least Common Multiple of 31978 and 31994?

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 31978 and 31994 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31978 and 31994, than apply into the LCM equation.

GCF(31978,31994) = 2
LCM(31978,31994) = ( 31978 × 31994) / 2
LCM(31978,31994) = 1023104132 / 2
LCM(31978,31994) = 511552066

Least Common Multiple (LCM) of 31978 and 31994 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31978 and 31994. First we will calculate the prime factors of 31978 and 31994.

Prime Factorization of 31978

Prime Factorization of 31994

Now multiplying the highest exponent prime factors to calculate the LCM of 31978 and 31994.

LCM(31978,31994) = 2¹ × 59¹ × 271¹ × 17¹ × 941¹
LCM(31978,31994) = 511552066