What is the Least Common Multiple of 206 and 222?
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 206 and 222 is 22866.
LCM(206,222) = 22866
Least Common Multiple of 206 and 222 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 206 and 222, than apply into the LCM equation.
GCF(206,222) = 2
LCM(206,222) = ( 206 × 222) / 2
LCM(206,222) = 45732 / 2
LCM(206,222) = 22866
Least Common Multiple (LCM) of 206 and 222 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 206 and 222. First we will calculate the prime factors of 206 and 222.
Prime Factorization of 206
Prime factors of 206 are 2, 103. Prime factorization of 206 in exponential form is:
206 = 21 × 1031
Prime Factorization of 222
Prime factors of 222 are 2, 3, 37. Prime factorization of 222 in exponential form is:
222 = 21 × 31 × 371
Now multiplying the highest exponent prime factors to calculate the LCM of 206 and 222.
LCM(206,222) = 21 × 1031 × 31 × 371
LCM(206,222) = 22866
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