What is the Least Common Multiple of 46 and 57?
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 46 and 57 is 2622.
LCM(46,57) = 2622
Least Common Multiple of 46 and 57 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46 and 57, than apply into the LCM equation.
GCF(46,57) = 1
LCM(46,57) = ( 46 × 57) / 1
LCM(46,57) = 2622 / 1
LCM(46,57) = 2622
Least Common Multiple (LCM) of 46 and 57 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 46 and 57. First we will calculate the prime factors of 46 and 57.
Prime Factorization of 46
Prime factors of 46 are 2, 23. Prime factorization of 46 in exponential form is:
46 = 21 × 231
Prime Factorization of 57
Prime factors of 57 are 3, 19. Prime factorization of 57 in exponential form is:
57 = 31 × 191
Now multiplying the highest exponent prime factors to calculate the LCM of 46 and 57.
LCM(46,57) = 21 × 231 × 31 × 191
LCM(46,57) = 2622