What is the Least Common Multiple of 5 and 21?
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 5 and 21 is 105.
LCM(5,21) = 105
Least Common Multiple of 5 and 21 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5 and 21, than apply into the LCM equation.
GCF(5,21) = 1
LCM(5,21) = ( 5 × 21) / 1
LCM(5,21) = 105 / 1
LCM(5,21) = 105
Least Common Multiple (LCM) of 5 and 21 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 21. First we will calculate the prime factors of 5 and 21.
Prime Factorization of 5
Prime factors of 5 are 5. Prime factorization of 5 in exponential form is:
5 = 51
Prime Factorization of 21
Prime factors of 21 are 3, 7. Prime factorization of 21 in exponential form is:
21 = 31 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 5 and 21.
LCM(5,21) = 51 × 31 × 71
LCM(5,21) = 105