What is the Least Common Multiple of 34 and 42?
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 42 is 714.
LCM(34,42) = 714
Least Common Multiple of 34 and 42 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 42, than apply into the LCM equation.
GCF(34,42) = 2
LCM(34,42) = ( 34 × 42) / 2
LCM(34,42) = 1428 / 2
LCM(34,42) = 714
Least Common Multiple (LCM) of 34 and 42 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 34 and 42. First we will calculate the prime factors of 34 and 42.
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 42
Prime factors of 42 are 2, 3, 7. Prime factorization of 42 in exponential form is:
42 = 21 × 31 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 34 and 42.
LCM(34,42) = 21 × 171 × 31 × 71
LCM(34,42) = 714