What is the Least Common Multiple of 10 and 23?
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 23 is 230.
LCM(10,23) = 230
Least Common Multiple of 10 and 23 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 23, than apply into the LCM equation.
GCF(10,23) = 1
LCM(10,23) = ( 10 × 23) / 1
LCM(10,23) = 230 / 1
LCM(10,23) = 230
Least Common Multiple (LCM) of 10 and 23 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 23. First we will calculate the prime factors of 10 and 23.
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 23
Prime factors of 23 are 23. Prime factorization of 23 in exponential form is:
23 = 231
Now multiplying the highest exponent prime factors to calculate the LCM of 10 and 23.
LCM(10,23) = 21 × 51 × 231
LCM(10,23) = 230