What is the Least Common Multiple of 993 and 1001?
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 993 and 1001 is 993993.
LCM(993,1001) = 993993
Least Common Multiple of 993 and 1001 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 993 and 1001, than apply into the LCM equation.
GCF(993,1001) = 1
LCM(993,1001) = ( 993 × 1001) / 1
LCM(993,1001) = 993993 / 1
LCM(993,1001) = 993993
Least Common Multiple (LCM) of 993 and 1001 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 993 and 1001. First we will calculate the prime factors of 993 and 1001.
Prime Factorization of 993
Prime factors of 993 are 3, 331. Prime factorization of 993 in exponential form is:
993 = 31 × 3311
Prime Factorization of 1001
Prime factors of 1001 are 7, 11, 13. Prime factorization of 1001 in exponential form is:
1001 = 71 × 111 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 993 and 1001.
LCM(993,1001) = 31 × 3311 × 71 × 111 × 131
LCM(993,1001) = 993993
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