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What is the Least Common Multiple of 75960 and 75974?

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 75960 and 75974 is 2885492520.

LCM(75960,75974) = 2885492520

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Least Common Multiple of 75960 and 75974 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75960 and 75974, than apply into the LCM equation.

GCF(75960,75974) = 2
LCM(75960,75974) = ( 75960 × 75974) / 2
LCM(75960,75974) = 5770985040 / 2
LCM(75960,75974) = 2885492520

Least Common Multiple (LCM) of 75960 and 75974 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75960 and 75974. First we will calculate the prime factors of 75960 and 75974.

Prime Factorization of 75960

Prime factors of 75960 are 2, 3, 5, 211. Prime factorization of 75960 in exponential form is:

75960 = 23 × 32 × 51 × 2111

Prime Factorization of 75974

Prime factors of 75974 are 2, 37987. Prime factorization of 75974 in exponential form is:

75974 = 21 × 379871

Now multiplying the highest exponent prime factors to calculate the LCM of 75960 and 75974.

LCM(75960,75974) = 23 × 32 × 51 × 2111 × 379871
LCM(75960,75974) = 2885492520