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What is the Least Common Multiple of 67110 and 67114?

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 67110 and 67114 is 2252010270.

LCM(67110,67114) = 2252010270

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Least Common Multiple of 67110 and 67114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67110 and 67114, than apply into the LCM equation.

GCF(67110,67114) = 2
LCM(67110,67114) = ( 67110 × 67114) / 2
LCM(67110,67114) = 4504020540 / 2
LCM(67110,67114) = 2252010270

Least Common Multiple (LCM) of 67110 and 67114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67110 and 67114. First we will calculate the prime factors of 67110 and 67114.

Prime Factorization of 67110

Prime factors of 67110 are 2, 3, 5, 2237. Prime factorization of 67110 in exponential form is:

67110 = 21 × 31 × 51 × 22371

Prime Factorization of 67114

Prime factors of 67114 are 2, 23, 1459. Prime factorization of 67114 in exponential form is:

67114 = 21 × 231 × 14591

Now multiplying the highest exponent prime factors to calculate the LCM of 67110 and 67114.

LCM(67110,67114) = 21 × 31 × 51 × 22371 × 231 × 14591
LCM(67110,67114) = 2252010270