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What is the Least Common Multiple of 10959 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 (LCM) of 10959 and 10974 is 40088022.

LCM(10959,10974) = 40088022

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Least Common Multiple of 10959 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 10959 and 10974, than apply into the LCM equation.

GCF(10959,10974) = 3
LCM(10959,10974) = ( 10959 × 10974) / 3
LCM(10959,10974) = 120264066 / 3
LCM(10959,10974) = 40088022

Least Common Multiple (LCM) of 10959 and 10974 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10959 and 10974. First we will calculate the prime factors of 10959 and 10974.

Prime Factorization of 10959

Prime factors of 10959 are 3, 13, 281. Prime factorization of 10959 in exponential form is:

10959 = 31 × 131 × 2811

Prime Factorization of 10974

Prime factors of 10974 are 2, 3, 31, 59. Prime factorization of 10974 in exponential form is:

10974 = 21 × 31 × 311 × 591

Now multiplying the highest exponent prime factors to calculate the LCM of 10959 and 10974.

LCM(10959,10974) = 31 × 131 × 2811 × 21 × 311 × 591
LCM(10959,10974) = 40088022