What is the Least Common Multiple of 3 and 19?
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 3 and 19 is 57.
LCM(3,19) = 57
Least Common Multiple of 3 and 19 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 19, than apply into the LCM equation.
GCF(3,19) = 1
LCM(3,19) = ( 3 × 19) / 1
LCM(3,19) = 57 / 1
LCM(3,19) = 57
Least Common Multiple (LCM) of 3 and 19 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 19. First we will calculate the prime factors of 3 and 19.
Prime Factorization of 3
Prime factors of 3 are 3. Prime factorization of 3 in exponential form is:
3 = 31
Prime Factorization of 19
Prime factors of 19 are 19. Prime factorization of 19 in exponential form is:
19 = 191
Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 19.
LCM(3,19) = 31 × 191
LCM(3,19) = 57