What is the Least Common Multiple of 48 and 68?
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 48 and 68 is 816.
LCM(48,68) = 816
Least Common Multiple of 48 and 68 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48 and 68, than apply into the LCM equation.
GCF(48,68) = 4
LCM(48,68) = ( 48 × 68) / 4
LCM(48,68) = 3264 / 4
LCM(48,68) = 816
Least Common Multiple (LCM) of 48 and 68 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 48 and 68. First we will calculate the prime factors of 48 and 68.
Prime Factorization of 48
Prime factors of 48 are 2, 3. Prime factorization of 48 in exponential form is:
48 = 24 × 31
Prime Factorization of 68
Prime factors of 68 are 2, 17. Prime factorization of 68 in exponential form is:
68 = 22 × 171
Now multiplying the highest exponent prime factors to calculate the LCM of 48 and 68.
LCM(48,68) = 24 × 31 × 171
LCM(48,68) = 816