What is the Least Common Multiple of 21 and 31?
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 21 and 31 is 651.
LCM(21,31) = 651
Least Common Multiple of 21 and 31 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21 and 31, than apply into the LCM equation.
GCF(21,31) = 1
LCM(21,31) = ( 21 × 31) / 1
LCM(21,31) = 651 / 1
LCM(21,31) = 651
Least Common Multiple (LCM) of 21 and 31 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 31. First we will calculate the prime factors of 21 and 31.
Prime Factorization of 21
Prime factors of 21 are 3, 7. Prime factorization of 21 in exponential form is:
21 = 31 × 71
Prime Factorization of 31
Prime factors of 31 are 31. Prime factorization of 31 in exponential form is:
31 = 311
Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 31.
LCM(21,31) = 31 × 71 × 311
LCM(21,31) = 651