What is the Least Common Multiple of 304 and 310?
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 304 and 310 is 47120.
LCM(304,310) = 47120
Least Common Multiple of 304 and 310 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 304 and 310, than apply into the LCM equation.
GCF(304,310) = 2
LCM(304,310) = ( 304 × 310) / 2
LCM(304,310) = 94240 / 2
LCM(304,310) = 47120
Least Common Multiple (LCM) of 304 and 310 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 304 and 310. First we will calculate the prime factors of 304 and 310.
Prime Factorization of 304
Prime factors of 304 are 2, 19. Prime factorization of 304 in exponential form is:
304 = 24 × 191
Prime Factorization of 310
Prime factors of 310 are 2, 5, 31. Prime factorization of 310 in exponential form is:
310 = 21 × 51 × 311
Now multiplying the highest exponent prime factors to calculate the LCM of 304 and 310.
LCM(304,310) = 24 × 191 × 51 × 311
LCM(304,310) = 47120
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