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What is the Least Common Multiple of 10969 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 10969 and 10974 is 120373806.

LCM(10969,10974) = 120373806

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Least Common Multiple of 10969 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 10969 and 10974, than apply into the LCM equation.

GCF(10969,10974) = 1
LCM(10969,10974) = ( 10969 × 10974) / 1
LCM(10969,10974) = 120373806 / 1
LCM(10969,10974) = 120373806

Least Common Multiple (LCM) of 10969 and 10974 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10969 and 10974. First we will calculate the prime factors of 10969 and 10974.

Prime Factorization of 10969

Prime factors of 10969 are 7, 1567. Prime factorization of 10969 in exponential form is:

10969 = 71 × 15671

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 10969 and 10974.

LCM(10969,10974) = 71 × 15671 × 21 × 31 × 311 × 591
LCM(10969,10974) = 120373806