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What is the Least Common Multiple of 400 and 412?

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 400 and 412 is 41200.

LCM(400,412) = 41200

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Least Common Multiple of 400 and 412 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 400 and 412, than apply into the LCM equation.

GCF(400,412) = 4
LCM(400,412) = ( 400 × 412) / 4
LCM(400,412) = 164800 / 4
LCM(400,412) = 41200

Least Common Multiple (LCM) of 400 and 412 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 400 and 412. First we will calculate the prime factors of 400 and 412.

Prime Factorization of 400

Prime factors of 400 are 2, 5. Prime factorization of 400 in exponential form is:

400 = 24 × 52

Prime Factorization of 412

Prime factors of 412 are 2, 103. Prime factorization of 412 in exponential form is:

412 = 22 × 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 400 and 412.

LCM(400,412) = 24 × 52 × 1031
LCM(400,412) = 41200