What is the Least Common Multiple of 31 and 47?
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 31 and 47 is 1457.
LCM(31,47) = 1457
Least Common Multiple of 31 and 47 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31 and 47, than apply into the LCM equation.
GCF(31,47) = 1
LCM(31,47) = ( 31 × 47) / 1
LCM(31,47) = 1457 / 1
LCM(31,47) = 1457
Least Common Multiple (LCM) of 31 and 47 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 31 and 47. First we will calculate the prime factors of 31 and 47.
Prime Factorization of 31
Prime factors of 31 are 31. Prime factorization of 31 in exponential form is:
31 = 311
Prime Factorization of 47
Prime factors of 47 are 47. Prime factorization of 47 in exponential form is:
47 = 471
Now multiplying the highest exponent prime factors to calculate the LCM of 31 and 47.
LCM(31,47) = 311 × 471
LCM(31,47) = 1457