What is the Least Common Multiple of 765 and 785?
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 785 is 120105.
LCM(765,785) = 120105
Least Common Multiple of 765 and 785 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 785, than apply into the LCM equation.
GCF(765,785) = 5
LCM(765,785) = ( 765 × 785) / 5
LCM(765,785) = 600525 / 5
LCM(765,785) = 120105
Least Common Multiple (LCM) of 765 and 785 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 765 and 785. First we will calculate the prime factors of 765 and 785.
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 785
Prime factors of 785 are 5, 157. Prime factorization of 785 in exponential form is:
785 = 51 × 1571
Now multiplying the highest exponent prime factors to calculate the LCM of 765 and 785.
LCM(765,785) = 32 × 51 × 171 × 1571
LCM(765,785) = 120105
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