What is the Least Common Multiple of 8 and 14?
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 8 and 14 is 56.
LCM(8,14) = 56
Least Common Multiple of 8 and 14 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8 and 14, than apply into the LCM equation.
GCF(8,14) = 2
LCM(8,14) = ( 8 × 14) / 2
LCM(8,14) = 112 / 2
LCM(8,14) = 56
Least Common Multiple (LCM) of 8 and 14 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 14. First we will calculate the prime factors of 8 and 14.
Prime Factorization of 8
Prime factors of 8 are 2. Prime factorization of 8 in exponential form is:
8 = 23
Prime Factorization of 14
Prime factors of 14 are 2, 7. Prime factorization of 14 in exponential form is:
14 = 21 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 14.
LCM(8,14) = 23 × 71
LCM(8,14) = 56