What is the Least Common Multiple of 7 and 24?
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 7 and 24 is 168.
LCM(7,24) = 168
Least Common Multiple of 7 and 24 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7 and 24, than apply into the LCM equation.
GCF(7,24) = 1
LCM(7,24) = ( 7 × 24) / 1
LCM(7,24) = 168 / 1
LCM(7,24) = 168
Least Common Multiple (LCM) of 7 and 24 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 7 and 24. First we will calculate the prime factors of 7 and 24.
Prime Factorization of 7
Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:
7 = 71
Prime Factorization of 24
Prime factors of 24 are 2, 3. Prime factorization of 24 in exponential form is:
24 = 23 × 31
Now multiplying the highest exponent prime factors to calculate the LCM of 7 and 24.
LCM(7,24) = 71 × 23 × 31
LCM(7,24) = 168