What is the Least Common Multiple of 54 and 74?
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 74 is 1998.
LCM(54,74) = 1998
Least Common Multiple of 54 and 74 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 74, than apply into the LCM equation.
GCF(54,74) = 2
LCM(54,74) = ( 54 × 74) / 2
LCM(54,74) = 3996 / 2
LCM(54,74) = 1998
Least Common Multiple (LCM) of 54 and 74 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 74. First we will calculate the prime factors of 54 and 74.
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 74
Prime factors of 74 are 2, 37. Prime factorization of 74 in exponential form is:
74 = 21 × 371
Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 74.
LCM(54,74) = 21 × 33 × 371
LCM(54,74) = 1998