What is the Least Common Multiple of 305 and 322?
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 305 and 322 is 98210.
LCM(305,322) = 98210
Least Common Multiple of 305 and 322 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 305 and 322, than apply into the LCM equation.
GCF(305,322) = 1
LCM(305,322) = ( 305 × 322) / 1
LCM(305,322) = 98210 / 1
LCM(305,322) = 98210
Least Common Multiple (LCM) of 305 and 322 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 305 and 322. First we will calculate the prime factors of 305 and 322.
Prime Factorization of 305
Prime factors of 305 are 5, 61. Prime factorization of 305 in exponential form is:
305 = 51 × 611
Prime Factorization of 322
Prime factors of 322 are 2, 7, 23. Prime factorization of 322 in exponential form is:
322 = 21 × 71 × 231
Now multiplying the highest exponent prime factors to calculate the LCM of 305 and 322.
LCM(305,322) = 51 × 611 × 21 × 71 × 231
LCM(305,322) = 98210
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