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What is the Least Common Multiple of 782 and 802?

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 782 and 802 is 313582.

LCM(782,802) = 313582

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Least Common Multiple of 782 and 802 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 782 and 802, than apply into the LCM equation.

GCF(782,802) = 2
LCM(782,802) = ( 782 × 802) / 2
LCM(782,802) = 627164 / 2
LCM(782,802) = 313582

Least Common Multiple (LCM) of 782 and 802 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 782 and 802. First we will calculate the prime factors of 782 and 802.

Prime Factorization of 782

Prime factors of 782 are 2, 17, 23. Prime factorization of 782 in exponential form is:

782 = 21 × 171 × 231

Prime Factorization of 802

Prime factors of 802 are 2, 401. Prime factorization of 802 in exponential form is:

802 = 21 × 4011

Now multiplying the highest exponent prime factors to calculate the LCM of 782 and 802.

LCM(782,802) = 21 × 171 × 231 × 4011
LCM(782,802) = 313582