What is the Least Common Multiple of 782 and 789?
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 789 is 616998.
LCM(782,789) = 616998
Least Common Multiple of 782 and 789 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 789, than apply into the LCM equation.
GCF(782,789) = 1
LCM(782,789) = ( 782 × 789) / 1
LCM(782,789) = 616998 / 1
LCM(782,789) = 616998
Least Common Multiple (LCM) of 782 and 789 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 782 and 789. First we will calculate the prime factors of 782 and 789.
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 789
Prime factors of 789 are 3, 263. Prime factorization of 789 in exponential form is:
789 = 31 × 2631
Now multiplying the highest exponent prime factors to calculate the LCM of 782 and 789.
LCM(782,789) = 21 × 171 × 231 × 31 × 2631
LCM(782,789) = 616998
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