What is the Least Common Multiple of 14 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 14 and 21 is 42.
LCM(14,21) = 42
Least Common Multiple of 14 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 14 and 21, than apply into the LCM equation.
GCF(14,21) = 7
LCM(14,21) = ( 14 × 21) / 7
LCM(14,21) = 294 / 7
LCM(14,21) = 42
Least Common Multiple (LCM) of 14 and 21 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 14 and 21. First we will calculate the prime factors of 14 and 21.
Prime Factorization of 14
Prime factors of 14 are 2, 7. Prime factorization of 14 in exponential form is:
14 = 21 × 71
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 14 and 21.
LCM(14,21) = 21 × 71 × 31
LCM(14,21) = 42