What is the Least Common Multiple of 765 and 780?
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 765 and 780 is 39780.
LCM(765,780) = 39780
Least Common Multiple of 765 and 780 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 765 and 780, than apply into the LCM equation.
GCF(765,780) = 15
LCM(765,780) = ( 765 × 780) / 15
LCM(765,780) = 596700 / 15
LCM(765,780) = 39780
Least Common Multiple (LCM) of 765 and 780 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 765 and 780. First we will calculate the prime factors of 765 and 780.
Prime Factorization of 765
Prime factors of 765 are 3, 5, 17. Prime factorization of 765 in exponential form is:
765 = 32 × 51 × 171
Prime Factorization of 780
Prime factors of 780 are 2, 3, 5, 13. Prime factorization of 780 in exponential form is:
780 = 22 × 31 × 51 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 765 and 780.
LCM(765,780) = 32 × 51 × 171 × 22 × 131
LCM(765,780) = 39780
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