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What is the Least Common Multiple of 48415 and 48420?

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 48415 and 48420 is 468850860.

LCM(48415,48420) = 468850860

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Least Common Multiple of 48415 and 48420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48415 and 48420, than apply into the LCM equation.

GCF(48415,48420) = 5
LCM(48415,48420) = ( 48415 × 48420) / 5
LCM(48415,48420) = 2344254300 / 5
LCM(48415,48420) = 468850860

Least Common Multiple (LCM) of 48415 and 48420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 48415 and 48420. First we will calculate the prime factors of 48415 and 48420.

Prime Factorization of 48415

Prime factors of 48415 are 5, 23, 421. Prime factorization of 48415 in exponential form is:

48415 = 51 × 231 × 4211

Prime Factorization of 48420

Prime factors of 48420 are 2, 3, 5, 269. Prime factorization of 48420 in exponential form is:

48420 = 22 × 32 × 51 × 2691

Now multiplying the highest exponent prime factors to calculate the LCM of 48415 and 48420.

LCM(48415,48420) = 51 × 231 × 4211 × 22 × 32 × 2691
LCM(48415,48420) = 468850860