What is the Least Common Multiple of 38 and 52?
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 38 and 52 is 988.
LCM(38,52) = 988
Least Common Multiple of 38 and 52 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38 and 52, than apply into the LCM equation.
GCF(38,52) = 2
LCM(38,52) = ( 38 × 52) / 2
LCM(38,52) = 1976 / 2
LCM(38,52) = 988
Least Common Multiple (LCM) of 38 and 52 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 38 and 52. First we will calculate the prime factors of 38 and 52.
Prime Factorization of 38
Prime factors of 38 are 2, 19. Prime factorization of 38 in exponential form is:
38 = 21 × 191
Prime Factorization of 52
Prime factors of 52 are 2, 13. Prime factorization of 52 in exponential form is:
52 = 22 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 38 and 52.
LCM(38,52) = 22 × 191 × 131
LCM(38,52) = 988