What is the Least Common Multiple of 6 and 90?
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 6 and 90 is 90.
LCM(6,90) = 90
Least Common Multiple of 6 and 90 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 90, than apply into the LCM equation.
GCF(6,90) = 6
LCM(6,90) = ( 6 × 90) / 6
LCM(6,90) = 540 / 6
LCM(6,90) = 90
Least Common Multiple (LCM) of 6 and 90 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 90. First we will calculate the prime factors of 6 and 90.
Prime Factorization of 6
Prime factors of 6 are 2, 3. Prime factorization of 6 in exponential form is:
6 = 21 × 31
Prime Factorization of 90
Prime factors of 90 are 2, 3, 5. Prime factorization of 90 in exponential form is:
90 = 21 × 32 × 51
Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 90.
LCM(6,90) = 21 × 32 × 51
LCM(6,90) = 90