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What is the Least Common Multiple of 1012 and 1030?

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 1012 and 1030 is 521180.

LCM(1012,1030) = 521180

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Least Common Multiple of 1012 and 1030 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1012 and 1030, than apply into the LCM equation.

GCF(1012,1030) = 2
LCM(1012,1030) = ( 1012 × 1030) / 2
LCM(1012,1030) = 1042360 / 2
LCM(1012,1030) = 521180

Least Common Multiple (LCM) of 1012 and 1030 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1012 and 1030. First we will calculate the prime factors of 1012 and 1030.

Prime Factorization of 1012

Prime factors of 1012 are 2, 11, 23. Prime factorization of 1012 in exponential form is:

1012 = 22 × 111 × 231

Prime Factorization of 1030

Prime factors of 1030 are 2, 5, 103. Prime factorization of 1030 in exponential form is:

1030 = 21 × 51 × 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 1012 and 1030.

LCM(1012,1030) = 22 × 111 × 231 × 51 × 1031
LCM(1012,1030) = 521180