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What is the Least Common Multiple of 1007 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 1007 and 1022 is 1029154.

LCM(1007,1022) = 1029154

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Least Common Multiple of 1007 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 1007 and 1022, than apply into the LCM equation.

GCF(1007,1022) = 1
LCM(1007,1022) = ( 1007 × 1022) / 1
LCM(1007,1022) = 1029154 / 1
LCM(1007,1022) = 1029154

Least Common Multiple (LCM) of 1007 and 1022 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1007 and 1022. First we will calculate the prime factors of 1007 and 1022.

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 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 1007 and 1022.

LCM(1007,1022) = 191 × 531 × 21 × 71 × 731
LCM(1007,1022) = 1029154