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What is the Least Common Multiple of 45983 and 46000?

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 45983 and 46000 is 2115218000.

LCM(45983,46000) = 2115218000

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Least Common Multiple of 45983 and 46000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45983 and 46000, than apply into the LCM equation.

GCF(45983,46000) = 1
LCM(45983,46000) = ( 45983 × 46000) / 1
LCM(45983,46000) = 2115218000 / 1
LCM(45983,46000) = 2115218000

Least Common Multiple (LCM) of 45983 and 46000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45983 and 46000. First we will calculate the prime factors of 45983 and 46000.

Prime Factorization of 45983

Prime factors of 45983 are 7, 6569. Prime factorization of 45983 in exponential form is:

45983 = 71 × 65691

Prime Factorization of 46000

Prime factors of 46000 are 2, 5, 23. Prime factorization of 46000 in exponential form is:

46000 = 24 × 53 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 45983 and 46000.

LCM(45983,46000) = 71 × 65691 × 24 × 53 × 231
LCM(45983,46000) = 2115218000