What is the Least Common Multiple of 26 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 26 and 14 is 182.
LCM(26,14) = 182
Least Common Multiple of 26 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 26 and 14, than apply into the LCM equation.
GCF(26,14) = 2
LCM(26,14) = ( 26 × 14) / 2
LCM(26,14) = 364 / 2
LCM(26,14) = 182
Least Common Multiple (LCM) of 26 and 14 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 26 and 14. First we will calculate the prime factors of 26 and 14.
Prime Factorization of 26
Prime factors of 26 are 2, 13. Prime factorization of 26 in exponential form is:
26 = 21 × 131
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 26 and 14.
LCM(26,14) = 21 × 131 × 71
LCM(26,14) = 182