What is the Least Common Multiple of 54 and 64?
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 54 and 64 is 1728.
LCM(54,64) = 1728
Least Common Multiple of 54 and 64 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54 and 64, than apply into the LCM equation.
GCF(54,64) = 2
LCM(54,64) = ( 54 × 64) / 2
LCM(54,64) = 3456 / 2
LCM(54,64) = 1728
Least Common Multiple (LCM) of 54 and 64 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 64. First we will calculate the prime factors of 54 and 64.
Prime Factorization of 54
Prime factors of 54 are 2, 3. Prime factorization of 54 in exponential form is:
54 = 21 × 33
Prime Factorization of 64
Prime factors of 64 are 2. Prime factorization of 64 in exponential form is:
64 = 26
Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 64.
LCM(54,64) = 26 × 33
LCM(54,64) = 1728