What is the Least Common Multiple of 665 and 675?
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 665 and 675 is 89775.
LCM(665,675) = 89775
Least Common Multiple of 665 and 675 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 665 and 675, than apply into the LCM equation.
GCF(665,675) = 5
LCM(665,675) = ( 665 × 675) / 5
LCM(665,675) = 448875 / 5
LCM(665,675) = 89775
Least Common Multiple (LCM) of 665 and 675 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 665 and 675. First we will calculate the prime factors of 665 and 675.
Prime Factorization of 665
Prime factors of 665 are 5, 7, 19. Prime factorization of 665 in exponential form is:
665 = 51 × 71 × 191
Prime Factorization of 675
Prime factors of 675 are 3, 5. Prime factorization of 675 in exponential form is:
675 = 33 × 52
Now multiplying the highest exponent prime factors to calculate the LCM of 665 and 675.
LCM(665,675) = 52 × 71 × 191 × 33
LCM(665,675) = 89775
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