What is the Least Common Multiple of 13 and 30?
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 13 and 30 is 390.
LCM(13,30) = 390
Least Common Multiple of 13 and 30 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13 and 30, than apply into the LCM equation.
GCF(13,30) = 1
LCM(13,30) = ( 13 × 30) / 1
LCM(13,30) = 390 / 1
LCM(13,30) = 390
Least Common Multiple (LCM) of 13 and 30 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 13 and 30. First we will calculate the prime factors of 13 and 30.
Prime Factorization of 13
Prime factors of 13 are 13. Prime factorization of 13 in exponential form is:
13 = 131
Prime Factorization of 30
Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:
30 = 21 × 31 × 51
Now multiplying the highest exponent prime factors to calculate the LCM of 13 and 30.
LCM(13,30) = 131 × 21 × 31 × 51
LCM(13,30) = 390