What is the Least Common Multiple of 10974 and 10989?

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 10974 and 10989 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10974 and 10989, than apply into the LCM equation.

GCF(10974,10989) = 3
LCM(10974,10989) = ( 10974 × 10989) / 3
LCM(10974,10989) = 120593286 / 3
LCM(10974,10989) = 40197762

Least Common Multiple (LCM) of 10974 and 10989 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10974 and 10989. First we will calculate the prime factors of 10974 and 10989.

Prime Factorization of 10974

Prime Factorization of 10989

Now multiplying the highest exponent prime factors to calculate the LCM of 10974 and 10989.

LCM(10974,10989) = 2¹ × 3³ × 31¹ × 59¹ × 11¹ × 37¹
LCM(10974,10989) = 40197762