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What is the Least Common Multiple of 1400 and 1412?

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 1400 and 1412 is 494200.

LCM(1400,1412) = 494200

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Least Common Multiple of 1400 and 1412 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1400 and 1412, than apply into the LCM equation.

GCF(1400,1412) = 4
LCM(1400,1412) = ( 1400 × 1412) / 4
LCM(1400,1412) = 1976800 / 4
LCM(1400,1412) = 494200

Least Common Multiple (LCM) of 1400 and 1412 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1400 and 1412. First we will calculate the prime factors of 1400 and 1412.

Prime Factorization of 1400

Prime factors of 1400 are 2, 5, 7. Prime factorization of 1400 in exponential form is:

1400 = 23 × 52 × 71

Prime Factorization of 1412

Prime factors of 1412 are 2, 353. Prime factorization of 1412 in exponential form is:

1412 = 22 × 3531

Now multiplying the highest exponent prime factors to calculate the LCM of 1400 and 1412.

LCM(1400,1412) = 23 × 52 × 71 × 3531
LCM(1400,1412) = 494200