What is the Least Common Multiple of 1014 and 1023?
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 1014 and 1023 is 345774.
LCM(1014,1023) = 345774
Least Common Multiple of 1014 and 1023 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1014 and 1023, than apply into the LCM equation.
GCF(1014,1023) = 3
LCM(1014,1023) = ( 1014 × 1023) / 3
LCM(1014,1023) = 1037322 / 3
LCM(1014,1023) = 345774
Least Common Multiple (LCM) of 1014 and 1023 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 1014 and 1023. First we will calculate the prime factors of 1014 and 1023.
Prime Factorization of 1014
Prime factors of 1014 are 2, 3, 13. Prime factorization of 1014 in exponential form is:
1014 = 21 × 31 × 132
Prime Factorization of 1023
Prime factors of 1023 are 3, 11, 31. Prime factorization of 1023 in exponential form is:
1023 = 31 × 111 × 311
Now multiplying the highest exponent prime factors to calculate the LCM of 1014 and 1023.
LCM(1014,1023) = 21 × 31 × 132 × 111 × 311
LCM(1014,1023) = 345774
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