What is the Least Common Multiple of 242 and 256?
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 242 and 256 is 30976.
LCM(242,256) = 30976
Least Common Multiple of 242 and 256 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 242 and 256, than apply into the LCM equation.
GCF(242,256) = 2
LCM(242,256) = ( 242 × 256) / 2
LCM(242,256) = 61952 / 2
LCM(242,256) = 30976
Least Common Multiple (LCM) of 242 and 256 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 242 and 256. First we will calculate the prime factors of 242 and 256.
Prime Factorization of 242
Prime factors of 242 are 2, 11. Prime factorization of 242 in exponential form is:
242 = 21 × 112
Prime Factorization of 256
Prime factors of 256 are 2. Prime factorization of 256 in exponential form is:
256 = 28
Now multiplying the highest exponent prime factors to calculate the LCM of 242 and 256.
LCM(242,256) = 28 × 112
LCM(242,256) = 30976
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