What is the Least Common Multiple of 10965 and 10974?

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 10965 and 10974 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10965 and 10974, than apply into the LCM equation.

GCF(10965,10974) = 3
LCM(10965,10974) = ( 10965 × 10974) / 3
LCM(10965,10974) = 120329910 / 3
LCM(10965,10974) = 40109970

Least Common Multiple (LCM) of 10965 and 10974 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10965 and 10974. First we will calculate the prime factors of 10965 and 10974.

Prime Factorization of 10965

Prime Factorization of 10974

Now multiplying the highest exponent prime factors to calculate the LCM of 10965 and 10974.

LCM(10965,10974) = 3¹ × 5¹ × 17¹ × 43¹ × 2¹ × 31¹ × 59¹
LCM(10965,10974) = 40109970