What is the Least Common Multiple of 39 and 51?
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 51 is 663.
LCM(39,51) = 663
Least Common Multiple of 39 and 51 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 51, than apply into the LCM equation.
GCF(39,51) = 3
LCM(39,51) = ( 39 × 51) / 3
LCM(39,51) = 1989 / 3
LCM(39,51) = 663
Least Common Multiple (LCM) of 39 and 51 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 39 and 51. First we will calculate the prime factors of 39 and 51.
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 51
Prime factors of 51 are 3, 17. Prime factorization of 51 in exponential form is:
51 = 31 × 171
Now multiplying the highest exponent prime factors to calculate the LCM of 39 and 51.
LCM(39,51) = 31 × 131 × 171
LCM(39,51) = 663