What is the Least Common Multiple of 24 and 36?
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 24 and 36 is 72.
LCM(24,36) = 72
Least Common Multiple of 24 and 36 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 24 and 36, than apply into the LCM equation.
GCF(24,36) = 12
LCM(24,36) = ( 24 × 36) / 12
LCM(24,36) = 864 / 12
LCM(24,36) = 72
Least Common Multiple (LCM) of 24 and 36 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 24 and 36. First we will calculate the prime factors of 24 and 36.
Prime Factorization of 24
Prime factors of 24 are 2, 3. Prime factorization of 24 in exponential form is:
24 = 23 × 31
Prime Factorization of 36
Prime factors of 36 are 2, 3. Prime factorization of 36 in exponential form is:
36 = 22 × 32
Now multiplying the highest exponent prime factors to calculate the LCM of 24 and 36.
LCM(24,36) = 23 × 32
LCM(24,36) = 72