What is the Least Common Multiple of 51 and 55?
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 51 and 55 is 2805.
LCM(51,55) = 2805
Least Common Multiple of 51 and 55 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51 and 55, than apply into the LCM equation.
GCF(51,55) = 1
LCM(51,55) = ( 51 × 55) / 1
LCM(51,55) = 2805 / 1
LCM(51,55) = 2805
Least Common Multiple (LCM) of 51 and 55 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 51 and 55. First we will calculate the prime factors of 51 and 55.
Prime Factorization of 51
Prime factors of 51 are 3, 17. Prime factorization of 51 in exponential form is:
51 = 31 × 171
Prime Factorization of 55
Prime factors of 55 are 5, 11. Prime factorization of 55 in exponential form is:
55 = 51 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 51 and 55.
LCM(51,55) = 31 × 171 × 51 × 111
LCM(51,55) = 2805