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What is the Least Common Multiple of 56400 and 56419?

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 56400 and 56419 is 3182031600.

LCM(56400,56419) = 3182031600

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Least Common Multiple of 56400 and 56419 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 56400 and 56419, than apply into the LCM equation.

GCF(56400,56419) = 1
LCM(56400,56419) = ( 56400 × 56419) / 1
LCM(56400,56419) = 3182031600 / 1
LCM(56400,56419) = 3182031600

Least Common Multiple (LCM) of 56400 and 56419 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 56400 and 56419. First we will calculate the prime factors of 56400 and 56419.

Prime Factorization of 56400

Prime factors of 56400 are 2, 3, 5, 47. Prime factorization of 56400 in exponential form is:

56400 = 24 × 31 × 52 × 471

Prime Factorization of 56419

Prime factors of 56419 are 11, 23, 223. Prime factorization of 56419 in exponential form is:

56419 = 111 × 231 × 2231

Now multiplying the highest exponent prime factors to calculate the LCM of 56400 and 56419.

LCM(56400,56419) = 24 × 31 × 52 × 471 × 111 × 231 × 2231
LCM(56400,56419) = 3182031600