What is the Least Common Multiple of 57 and 66?
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 57 and 66 is 1254.
LCM(57,66) = 1254
Least Common Multiple of 57 and 66 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57 and 66, than apply into the LCM equation.
GCF(57,66) = 3
LCM(57,66) = ( 57 × 66) / 3
LCM(57,66) = 3762 / 3
LCM(57,66) = 1254
Least Common Multiple (LCM) of 57 and 66 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 57 and 66. First we will calculate the prime factors of 57 and 66.
Prime Factorization of 57
Prime factors of 57 are 3, 19. Prime factorization of 57 in exponential form is:
57 = 31 × 191
Prime Factorization of 66
Prime factors of 66 are 2, 3, 11. Prime factorization of 66 in exponential form is:
66 = 21 × 31 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 57 and 66.
LCM(57,66) = 31 × 191 × 21 × 111
LCM(57,66) = 1254