What is the Least Common Multiple of 1014 and 1034?
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 1034 is 524238.
LCM(1014,1034) = 524238
Least Common Multiple of 1014 and 1034 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 1034, than apply into the LCM equation.
GCF(1014,1034) = 2
LCM(1014,1034) = ( 1014 × 1034) / 2
LCM(1014,1034) = 1048476 / 2
LCM(1014,1034) = 524238
Least Common Multiple (LCM) of 1014 and 1034 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 1014 and 1034. First we will calculate the prime factors of 1014 and 1034.
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 1034
Prime factors of 1034 are 2, 11, 47. Prime factorization of 1034 in exponential form is:
1034 = 21 × 111 × 471
Now multiplying the highest exponent prime factors to calculate the LCM of 1014 and 1034.
LCM(1014,1034) = 21 × 31 × 132 × 111 × 471
LCM(1014,1034) = 524238
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