What is the Least Common Multiple of 10 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 10 and 30 is 30.
LCM(10,30) = 30
Least Common Multiple of 10 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 10 and 30, than apply into the LCM equation.
GCF(10,30) = 10
LCM(10,30) = ( 10 × 30) / 10
LCM(10,30) = 300 / 10
LCM(10,30) = 30
Least Common Multiple (LCM) of 10 and 30 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 30. First we will calculate the prime factors of 10 and 30.
Prime Factorization of 10
Prime factors of 10 are 2, 5. Prime factorization of 10 in exponential form is:
10 = 21 × 51
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 10 and 30.
LCM(10,30) = 21 × 51 × 31
LCM(10,30) = 30