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What is the Least Common Multiple of 7954 and 7974?

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 7954 and 7974 is 31712598.

LCM(7954,7974) = 31712598

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Least Common Multiple of 7954 and 7974 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7954 and 7974, than apply into the LCM equation.

GCF(7954,7974) = 2
LCM(7954,7974) = ( 7954 × 7974) / 2
LCM(7954,7974) = 63425196 / 2
LCM(7954,7974) = 31712598

Least Common Multiple (LCM) of 7954 and 7974 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7954 and 7974. First we will calculate the prime factors of 7954 and 7974.

Prime Factorization of 7954

Prime factors of 7954 are 2, 41, 97. Prime factorization of 7954 in exponential form is:

7954 = 21 × 411 × 971

Prime Factorization of 7974

Prime factors of 7974 are 2, 3, 443. Prime factorization of 7974 in exponential form is:

7974 = 21 × 32 × 4431

Now multiplying the highest exponent prime factors to calculate the LCM of 7954 and 7974.

LCM(7954,7974) = 21 × 411 × 971 × 32 × 4431
LCM(7954,7974) = 31712598