What is the Least Common Multiple of 756 and 765?
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 756 and 765 is 64260.
LCM(756,765) = 64260
Least Common Multiple of 756 and 765 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 756 and 765, than apply into the LCM equation.
GCF(756,765) = 9
LCM(756,765) = ( 756 × 765) / 9
LCM(756,765) = 578340 / 9
LCM(756,765) = 64260
Least Common Multiple (LCM) of 756 and 765 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 756 and 765. First we will calculate the prime factors of 756 and 765.
Prime Factorization of 756
Prime factors of 756 are 2, 3, 7. Prime factorization of 756 in exponential form is:
756 = 22 × 33 × 71
Prime Factorization of 765
Prime factors of 765 are 3, 5, 17. Prime factorization of 765 in exponential form is:
765 = 32 × 51 × 171
Now multiplying the highest exponent prime factors to calculate the LCM of 756 and 765.
LCM(756,765) = 22 × 33 × 71 × 51 × 171
LCM(756,765) = 64260
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