What is the Least Common Multiple of 31758 and 31776?

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 31758 and 31776 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31758 and 31776, than apply into the LCM equation.

GCF(31758,31776) = 6
LCM(31758,31776) = ( 31758 × 31776) / 6
LCM(31758,31776) = 1009142208 / 6
LCM(31758,31776) = 168190368

Least Common Multiple (LCM) of 31758 and 31776 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31758 and 31776. First we will calculate the prime factors of 31758 and 31776.

Prime Factorization of 31758

Prime Factorization of 31776

Now multiplying the highest exponent prime factors to calculate the LCM of 31758 and 31776.

LCM(31758,31776) = 2⁵ × 3¹ × 67¹ × 79¹ × 331¹
LCM(31758,31776) = 168190368