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What is the Least Common Multiple of 7140 and 7156?

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 7140 and 7156 is 12773460.

LCM(7140,7156) = 12773460

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Least Common Multiple of 7140 and 7156 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7140 and 7156, than apply into the LCM equation.

GCF(7140,7156) = 4
LCM(7140,7156) = ( 7140 × 7156) / 4
LCM(7140,7156) = 51093840 / 4
LCM(7140,7156) = 12773460

Least Common Multiple (LCM) of 7140 and 7156 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7140 and 7156. First we will calculate the prime factors of 7140 and 7156.

Prime Factorization of 7140

Prime factors of 7140 are 2, 3, 5, 7, 17. Prime factorization of 7140 in exponential form is:

7140 = 22 × 31 × 51 × 71 × 171

Prime Factorization of 7156

Prime factors of 7156 are 2, 1789. Prime factorization of 7156 in exponential form is:

7156 = 22 × 17891

Now multiplying the highest exponent prime factors to calculate the LCM of 7140 and 7156.

LCM(7140,7156) = 22 × 31 × 51 × 71 × 171 × 17891
LCM(7140,7156) = 12773460