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What is the Least Common Multiple of 1006 and 1010?

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 1006 and 1010 is 508030.

LCM(1006,1010) = 508030

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Least Common Multiple of 1006 and 1010 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1006 and 1010, than apply into the LCM equation.

GCF(1006,1010) = 2
LCM(1006,1010) = ( 1006 × 1010) / 2
LCM(1006,1010) = 1016060 / 2
LCM(1006,1010) = 508030

Least Common Multiple (LCM) of 1006 and 1010 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1006 and 1010. First we will calculate the prime factors of 1006 and 1010.

Prime Factorization of 1006

Prime factors of 1006 are 2, 503. Prime factorization of 1006 in exponential form is:

1006 = 21 × 5031

Prime Factorization of 1010

Prime factors of 1010 are 2, 5, 101. Prime factorization of 1010 in exponential form is:

1010 = 21 × 51 × 1011

Now multiplying the highest exponent prime factors to calculate the LCM of 1006 and 1010.

LCM(1006,1010) = 21 × 5031 × 51 × 1011
LCM(1006,1010) = 508030