What is the Least Common Multiple of 7 and 34?
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 7 and 34 is 238.
LCM(7,34) = 238
Least Common Multiple of 7 and 34 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7 and 34, than apply into the LCM equation.
GCF(7,34) = 1
LCM(7,34) = ( 7 × 34) / 1
LCM(7,34) = 238 / 1
LCM(7,34) = 238
Least Common Multiple (LCM) of 7 and 34 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 7 and 34. First we will calculate the prime factors of 7 and 34.
Prime Factorization of 7
Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:
7 = 71
Prime Factorization of 34
Prime factors of 34 are 2, 17. Prime factorization of 34 in exponential form is:
34 = 21 × 171
Now multiplying the highest exponent prime factors to calculate the LCM of 7 and 34.
LCM(7,34) = 71 × 21 × 171
LCM(7,34) = 238