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What is the Least Common Multiple of 1382 and 1400?

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 1382 and 1400 is 967400.

LCM(1382,1400) = 967400

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Least Common Multiple of 1382 and 1400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1382 and 1400, than apply into the LCM equation.

GCF(1382,1400) = 2
LCM(1382,1400) = ( 1382 × 1400) / 2
LCM(1382,1400) = 1934800 / 2
LCM(1382,1400) = 967400

Least Common Multiple (LCM) of 1382 and 1400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1382 and 1400. First we will calculate the prime factors of 1382 and 1400.

Prime Factorization of 1382

Prime factors of 1382 are 2, 691. Prime factorization of 1382 in exponential form is:

1382 = 21 × 6911

Prime Factorization of 1400

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

1400 = 23 × 52 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 1382 and 1400.

LCM(1382,1400) = 23 × 6911 × 52 × 71
LCM(1382,1400) = 967400