What is the Least Common Multiple of 39 and 54?
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 39 and 54 is 702.
LCM(39,54) = 702
Least Common Multiple of 39 and 54 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39 and 54, than apply into the LCM equation.
GCF(39,54) = 3
LCM(39,54) = ( 39 × 54) / 3
LCM(39,54) = 2106 / 3
LCM(39,54) = 702
Least Common Multiple (LCM) of 39 and 54 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 39 and 54. First we will calculate the prime factors of 39 and 54.
Prime Factorization of 39
Prime factors of 39 are 3, 13. Prime factorization of 39 in exponential form is:
39 = 31 × 131
Prime Factorization of 54
Prime factors of 54 are 2, 3. Prime factorization of 54 in exponential form is:
54 = 21 × 33
Now multiplying the highest exponent prime factors to calculate the LCM of 39 and 54.
LCM(39,54) = 33 × 131 × 21
LCM(39,54) = 702