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What is the Least Common Multiple of 1026 and 1032?

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 1026 and 1032 is 176472.

LCM(1026,1032) = 176472

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Least Common Multiple of 1026 and 1032 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1026 and 1032, than apply into the LCM equation.

GCF(1026,1032) = 6
LCM(1026,1032) = ( 1026 × 1032) / 6
LCM(1026,1032) = 1058832 / 6
LCM(1026,1032) = 176472

Least Common Multiple (LCM) of 1026 and 1032 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1026 and 1032. First we will calculate the prime factors of 1026 and 1032.

Prime Factorization of 1026

Prime factors of 1026 are 2, 3, 19. Prime factorization of 1026 in exponential form is:

1026 = 21 × 33 × 191

Prime Factorization of 1032

Prime factors of 1032 are 2, 3, 43. Prime factorization of 1032 in exponential form is:

1032 = 23 × 31 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 1026 and 1032.

LCM(1026,1032) = 23 × 33 × 191 × 431
LCM(1026,1032) = 176472