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What is the Least Common Multiple of 54002 and 54015?

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 54002 and 54015 is 224378310.

LCM(54002,54015) = 224378310

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Least Common Multiple of 54002 and 54015 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54002 and 54015, than apply into the LCM equation.

GCF(54002,54015) = 13
LCM(54002,54015) = ( 54002 × 54015) / 13
LCM(54002,54015) = 2916918030 / 13
LCM(54002,54015) = 224378310

Least Common Multiple (LCM) of 54002 and 54015 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54002 and 54015. First we will calculate the prime factors of 54002 and 54015.

Prime Factorization of 54002

Prime factors of 54002 are 2, 13, 31, 67. Prime factorization of 54002 in exponential form is:

54002 = 21 × 131 × 311 × 671

Prime Factorization of 54015

Prime factors of 54015 are 3, 5, 13, 277. Prime factorization of 54015 in exponential form is:

54015 = 31 × 51 × 131 × 2771

Now multiplying the highest exponent prime factors to calculate the LCM of 54002 and 54015.

LCM(54002,54015) = 21 × 131 × 311 × 671 × 31 × 51 × 2771
LCM(54002,54015) = 224378310