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What is the Least Common Multiple of 10965 and 10972?

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 10972 is 120307980.

LCM(10965,10972) = 120307980

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Least Common Multiple of 10965 and 10972 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 10972, than apply into the LCM equation.

GCF(10965,10972) = 1
LCM(10965,10972) = ( 10965 × 10972) / 1
LCM(10965,10972) = 120307980 / 1
LCM(10965,10972) = 120307980

Least Common Multiple (LCM) of 10965 and 10972 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10965 and 10972. First we will calculate the prime factors of 10965 and 10972.

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 10972

Prime factors of 10972 are 2, 13, 211. Prime factorization of 10972 in exponential form is:

10972 = 22 × 131 × 2111

Now multiplying the highest exponent prime factors to calculate the LCM of 10965 and 10972.

LCM(10965,10972) = 31 × 51 × 171 × 431 × 22 × 131 × 2111
LCM(10965,10972) = 120307980