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What is the Least Common Multiple of 392 and 402?

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 392 and 402 is 78792.

LCM(392,402) = 78792

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Least Common Multiple of 392 and 402 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 392 and 402, than apply into the LCM equation.

GCF(392,402) = 2
LCM(392,402) = ( 392 × 402) / 2
LCM(392,402) = 157584 / 2
LCM(392,402) = 78792

Least Common Multiple (LCM) of 392 and 402 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 392 and 402. First we will calculate the prime factors of 392 and 402.

Prime Factorization of 392

Prime factors of 392 are 2, 7. Prime factorization of 392 in exponential form is:

392 = 23 × 72

Prime Factorization of 402

Prime factors of 402 are 2, 3, 67. Prime factorization of 402 in exponential form is:

402 = 21 × 31 × 671

Now multiplying the highest exponent prime factors to calculate the LCM of 392 and 402.

LCM(392,402) = 23 × 72 × 31 × 671
LCM(392,402) = 78792