What is the Least Common Multiple of 15 and 28?
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 15 and 28 is 420.
LCM(15,28) = 420
Least Common Multiple of 15 and 28 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15 and 28, than apply into the LCM equation.
GCF(15,28) = 1
LCM(15,28) = ( 15 × 28) / 1
LCM(15,28) = 420 / 1
LCM(15,28) = 420
Least Common Multiple (LCM) of 15 and 28 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 15 and 28. First we will calculate the prime factors of 15 and 28.
Prime Factorization of 15
Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:
15 = 31 × 51
Prime Factorization of 28
Prime factors of 28 are 2, 7. Prime factorization of 28 in exponential form is:
28 = 22 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 15 and 28.
LCM(15,28) = 31 × 51 × 22 × 71
LCM(15,28) = 420