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What is the Least Common Multiple of 5092 and 5100?

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 5092 and 5100 is 6492300.

LCM(5092,5100) = 6492300

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Least Common Multiple of 5092 and 5100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5092 and 5100, than apply into the LCM equation.

GCF(5092,5100) = 4
LCM(5092,5100) = ( 5092 × 5100) / 4
LCM(5092,5100) = 25969200 / 4
LCM(5092,5100) = 6492300

Least Common Multiple (LCM) of 5092 and 5100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5092 and 5100. First we will calculate the prime factors of 5092 and 5100.

Prime Factorization of 5092

Prime factors of 5092 are 2, 19, 67. Prime factorization of 5092 in exponential form is:

5092 = 22 × 191 × 671

Prime Factorization of 5100

Prime factors of 5100 are 2, 3, 5, 17. Prime factorization of 5100 in exponential form is:

5100 = 22 × 31 × 52 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 5092 and 5100.

LCM(5092,5100) = 22 × 191 × 671 × 31 × 52 × 171
LCM(5092,5100) = 6492300