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What is the Least Common Multiple of 54200 and 54219?

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 54200 and 54219 is 2938669800.

LCM(54200,54219) = 2938669800

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Least Common Multiple of 54200 and 54219 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54200 and 54219, than apply into the LCM equation.

GCF(54200,54219) = 1
LCM(54200,54219) = ( 54200 × 54219) / 1
LCM(54200,54219) = 2938669800 / 1
LCM(54200,54219) = 2938669800

Least Common Multiple (LCM) of 54200 and 54219 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54200 and 54219. First we will calculate the prime factors of 54200 and 54219.

Prime Factorization of 54200

Prime factors of 54200 are 2, 5, 271. Prime factorization of 54200 in exponential form is:

54200 = 23 × 52 × 2711

Prime Factorization of 54219

Prime factors of 54219 are 3, 11, 31, 53. Prime factorization of 54219 in exponential form is:

54219 = 31 × 111 × 311 × 531

Now multiplying the highest exponent prime factors to calculate the LCM of 54200 and 54219.

LCM(54200,54219) = 23 × 52 × 2711 × 31 × 111 × 311 × 531
LCM(54200,54219) = 2938669800