What is the Least Common Multiple of 31968 and 31983?

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 31968 and 31983 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31968 and 31983, than apply into the LCM equation.

GCF(31968,31983) = 3
LCM(31968,31983) = ( 31968 × 31983) / 3
LCM(31968,31983) = 1022432544 / 3
LCM(31968,31983) = 340810848

Least Common Multiple (LCM) of 31968 and 31983 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31968 and 31983. First we will calculate the prime factors of 31968 and 31983.

Prime Factorization of 31968

Prime Factorization of 31983

Now multiplying the highest exponent prime factors to calculate the LCM of 31968 and 31983.

LCM(31968,31983) = 2⁵ × 3³ × 37¹ × 7¹ × 1523¹
LCM(31968,31983) = 340810848