What is the Least Common Multiple of 21 and 39?
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 39 is 273.
LCM(21,39) = 273
Least Common Multiple of 21 and 39 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 39, than apply into the LCM equation.
GCF(21,39) = 3
LCM(21,39) = ( 21 × 39) / 3
LCM(21,39) = 819 / 3
LCM(21,39) = 273
Least Common Multiple (LCM) of 21 and 39 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 39. First we will calculate the prime factors of 21 and 39.
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 39
Prime factors of 39 are 3, 13. Prime factorization of 39 in exponential form is:
39 = 31 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 39.
LCM(21,39) = 31 × 71 × 131
LCM(21,39) = 273