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What is the Least Common Multiple of 10965 and 10978?

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 (LCM) of 10965 and 10978 is 120373770.

LCM(10965,10978) = 120373770

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Least Common Multiple of 10965 and 10978 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 10978, than apply into the LCM equation.

GCF(10965,10978) = 1
LCM(10965,10978) = ( 10965 × 10978) / 1
LCM(10965,10978) = 120373770 / 1
LCM(10965,10978) = 120373770

Least Common Multiple (LCM) of 10965 and 10978 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10965 and 10978. First we will calculate the prime factors of 10965 and 10978.

Prime Factorization of 10965

Prime factors of 10965 are 3, 5, 17, 43. Prime factorization of 10965 in exponential form is:

10965 = 31 × 51 × 171 × 431

Prime Factorization of 10978

Prime factors of 10978 are 2, 11, 499. Prime factorization of 10978 in exponential form is:

10978 = 21 × 111 × 4991

Now multiplying the highest exponent prime factors to calculate the LCM of 10965 and 10978.

LCM(10965,10978) = 31 × 51 × 171 × 431 × 21 × 111 × 4991
LCM(10965,10978) = 120373770