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What is the Least Common Multiple of 75702 and 75714?

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 75702 and 75714 is 955283538.

LCM(75702,75714) = 955283538

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Least Common Multiple of 75702 and 75714 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75702 and 75714, than apply into the LCM equation.

GCF(75702,75714) = 6
LCM(75702,75714) = ( 75702 × 75714) / 6
LCM(75702,75714) = 5731701228 / 6
LCM(75702,75714) = 955283538

Least Common Multiple (LCM) of 75702 and 75714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75702 and 75714. First we will calculate the prime factors of 75702 and 75714.

Prime Factorization of 75702

Prime factors of 75702 are 2, 3, 11, 31, 37. Prime factorization of 75702 in exponential form is:

75702 = 21 × 31 × 111 × 311 × 371

Prime Factorization of 75714

Prime factors of 75714 are 2, 3, 12619. Prime factorization of 75714 in exponential form is:

75714 = 21 × 31 × 126191

Now multiplying the highest exponent prime factors to calculate the LCM of 75702 and 75714.

LCM(75702,75714) = 21 × 31 × 111 × 311 × 371 × 126191
LCM(75702,75714) = 955283538