What is the Least Common Multiple of 21 and 27?
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 27 is 189.
LCM(21,27) = 189
Least Common Multiple of 21 and 27 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 27, than apply into the LCM equation.
GCF(21,27) = 3
LCM(21,27) = ( 21 × 27) / 3
LCM(21,27) = 567 / 3
LCM(21,27) = 189
Least Common Multiple (LCM) of 21 and 27 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 27. First we will calculate the prime factors of 21 and 27.
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 27
Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:
27 = 33
Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 27.
LCM(21,27) = 33 × 71
LCM(21,27) = 189