What is the Least Common Multiple of 1006 and 1022?
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 1006 and 1022 is 514066.
LCM(1006,1022) = 514066
Least Common Multiple of 1006 and 1022 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1006 and 1022, than apply into the LCM equation.
GCF(1006,1022) = 2
LCM(1006,1022) = ( 1006 × 1022) / 2
LCM(1006,1022) = 1028132 / 2
LCM(1006,1022) = 514066
Least Common Multiple (LCM) of 1006 and 1022 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 1006 and 1022. First we will calculate the prime factors of 1006 and 1022.
Prime Factorization of 1006
Prime factors of 1006 are 2, 503. Prime factorization of 1006 in exponential form is:
1006 = 21 × 5031
Prime Factorization of 1022
Prime factors of 1022 are 2, 7, 73. Prime factorization of 1022 in exponential form is:
1022 = 21 × 71 × 731
Now multiplying the highest exponent prime factors to calculate the LCM of 1006 and 1022.
LCM(1006,1022) = 21 × 5031 × 71 × 731
LCM(1006,1022) = 514066
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