What is the Least Common Multiple of 1007 and 1016?
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 1007 and 1016 is 1023112.
LCM(1007,1016) = 1023112
Least Common Multiple of 1007 and 1016 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1007 and 1016, than apply into the LCM equation.
GCF(1007,1016) = 1
LCM(1007,1016) = ( 1007 × 1016) / 1
LCM(1007,1016) = 1023112 / 1
LCM(1007,1016) = 1023112
Least Common Multiple (LCM) of 1007 and 1016 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 1007 and 1016. First we will calculate the prime factors of 1007 and 1016.
Prime Factorization of 1007
Prime factors of 1007 are 19, 53. Prime factorization of 1007 in exponential form is:
1007 = 191 × 531
Prime Factorization of 1016
Prime factors of 1016 are 2, 127. Prime factorization of 1016 in exponential form is:
1016 = 23 × 1271
Now multiplying the highest exponent prime factors to calculate the LCM of 1007 and 1016.
LCM(1007,1016) = 191 × 531 × 23 × 1271
LCM(1007,1016) = 1023112
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