What is the Least Common Multiple of 54 and 71?
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 54 and 71 is 3834.
LCM(54,71) = 3834
Least Common Multiple of 54 and 71 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54 and 71, than apply into the LCM equation.
GCF(54,71) = 1
LCM(54,71) = ( 54 × 71) / 1
LCM(54,71) = 3834 / 1
LCM(54,71) = 3834
Least Common Multiple (LCM) of 54 and 71 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 71. First we will calculate the prime factors of 54 and 71.
Prime Factorization of 54
Prime factors of 54 are 2, 3. Prime factorization of 54 in exponential form is:
54 = 21 × 33
Prime Factorization of 71
Prime factors of 71 are 71. Prime factorization of 71 in exponential form is:
71 = 711
Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 71.
LCM(54,71) = 21 × 33 × 711
LCM(54,71) = 3834