What is the Least Common Multiple of 5 and 22?
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 5 and 22 is 110.
LCM(5,22) = 110
Least Common Multiple of 5 and 22 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5 and 22, than apply into the LCM equation.
GCF(5,22) = 1
LCM(5,22) = ( 5 × 22) / 1
LCM(5,22) = 110 / 1
LCM(5,22) = 110
Least Common Multiple (LCM) of 5 and 22 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 22. First we will calculate the prime factors of 5 and 22.
Prime Factorization of 5
Prime factors of 5 are 5. Prime factorization of 5 in exponential form is:
5 = 51
Prime Factorization of 22
Prime factors of 22 are 2, 11. Prime factorization of 22 in exponential form is:
22 = 21 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 5 and 22.
LCM(5,22) = 51 × 21 × 111
LCM(5,22) = 110