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What is the Least Common Multiple of 40000 and 40005?

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 40000 and 40005 is 320040000.

LCM(40000,40005) = 320040000

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Least Common Multiple of 40000 and 40005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40000 and 40005, than apply into the LCM equation.

GCF(40000,40005) = 5
LCM(40000,40005) = ( 40000 × 40005) / 5
LCM(40000,40005) = 1600200000 / 5
LCM(40000,40005) = 320040000

Least Common Multiple (LCM) of 40000 and 40005 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40000 and 40005. First we will calculate the prime factors of 40000 and 40005.

Prime Factorization of 40000

Prime factors of 40000 are 2, 5. Prime factorization of 40000 in exponential form is:

40000 = 26 × 54

Prime Factorization of 40005

Prime factors of 40005 are 3, 5, 7, 127. Prime factorization of 40005 in exponential form is:

40005 = 32 × 51 × 71 × 1271

Now multiplying the highest exponent prime factors to calculate the LCM of 40000 and 40005.

LCM(40000,40005) = 26 × 54 × 32 × 71 × 1271
LCM(40000,40005) = 320040000