What is the Least Common Multiple of 34 and 41?
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 34 and 41 is 1394.
LCM(34,41) = 1394
Least Common Multiple of 34 and 41 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34 and 41, than apply into the LCM equation.
GCF(34,41) = 1
LCM(34,41) = ( 34 × 41) / 1
LCM(34,41) = 1394 / 1
LCM(34,41) = 1394
Least Common Multiple (LCM) of 34 and 41 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 34 and 41. First we will calculate the prime factors of 34 and 41.
Prime Factorization of 34
Prime factors of 34 are 2, 17. Prime factorization of 34 in exponential form is:
34 = 21 × 171
Prime Factorization of 41
Prime factors of 41 are 41. Prime factorization of 41 in exponential form is:
41 = 411
Now multiplying the highest exponent prime factors to calculate the LCM of 34 and 41.
LCM(34,41) = 21 × 171 × 411
LCM(34,41) = 1394