What is the Least Common Multiple of 302 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 302 and 322 is 48622.
LCM(302,322) = 48622
Least Common Multiple of 302 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 302 and 322, than apply into the LCM equation.
GCF(302,322) = 2
LCM(302,322) = ( 302 × 322) / 2
LCM(302,322) = 97244 / 2
LCM(302,322) = 48622
Least Common Multiple (LCM) of 302 and 322 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 302 and 322. First we will calculate the prime factors of 302 and 322.
Prime Factorization of 302
Prime factors of 302 are 2, 151. Prime factorization of 302 in exponential form is:
302 = 21 × 1511
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 302 and 322.
LCM(302,322) = 21 × 1511 × 71 × 231
LCM(302,322) = 48622
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