What is the Least Common Multiple of 309 and 320?
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 309 and 320 is 98880.
LCM(309,320) = 98880
Least Common Multiple of 309 and 320 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 309 and 320, than apply into the LCM equation.
GCF(309,320) = 1
LCM(309,320) = ( 309 × 320) / 1
LCM(309,320) = 98880 / 1
LCM(309,320) = 98880
Least Common Multiple (LCM) of 309 and 320 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 309 and 320. First we will calculate the prime factors of 309 and 320.
Prime Factorization of 309
Prime factors of 309 are 3, 103. Prime factorization of 309 in exponential form is:
309 = 31 × 1031
Prime Factorization of 320
Prime factors of 320 are 2, 5. Prime factorization of 320 in exponential form is:
320 = 26 × 51
Now multiplying the highest exponent prime factors to calculate the LCM of 309 and 320.
LCM(309,320) = 31 × 1031 × 26 × 51
LCM(309,320) = 98880
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