What is the Least Common Multiple of 50 and 66?
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 50 and 66 is 1650.
LCM(50,66) = 1650
Least Common Multiple of 50 and 66 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 50 and 66, than apply into the LCM equation.
GCF(50,66) = 2
LCM(50,66) = ( 50 × 66) / 2
LCM(50,66) = 3300 / 2
LCM(50,66) = 1650
Least Common Multiple (LCM) of 50 and 66 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 50 and 66. First we will calculate the prime factors of 50 and 66.
Prime Factorization of 50
Prime factors of 50 are 2, 5. Prime factorization of 50 in exponential form is:
50 = 21 × 52
Prime Factorization of 66
Prime factors of 66 are 2, 3, 11. Prime factorization of 66 in exponential form is:
66 = 21 × 31 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 50 and 66.
LCM(50,66) = 21 × 52 × 31 × 111
LCM(50,66) = 1650