What is the Least Common Multiple of 3 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 3 and 22 is 66.
LCM(3,22) = 66
Least Common Multiple of 3 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 3 and 22, than apply into the LCM equation.
GCF(3,22) = 1
LCM(3,22) = ( 3 × 22) / 1
LCM(3,22) = 66 / 1
LCM(3,22) = 66
Least Common Multiple (LCM) of 3 and 22 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 22. First we will calculate the prime factors of 3 and 22.
Prime Factorization of 3
Prime factors of 3 are 3. Prime factorization of 3 in exponential form is:
3 = 31
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 3 and 22.
LCM(3,22) = 31 × 21 × 111
LCM(3,22) = 66