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What is the Least Common Multiple of 1128 and 1132?

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 1128 and 1132 is 319224.

LCM(1128,1132) = 319224

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Least Common Multiple of 1128 and 1132 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1128 and 1132, than apply into the LCM equation.

GCF(1128,1132) = 4
LCM(1128,1132) = ( 1128 × 1132) / 4
LCM(1128,1132) = 1276896 / 4
LCM(1128,1132) = 319224

Least Common Multiple (LCM) of 1128 and 1132 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1128 and 1132. First we will calculate the prime factors of 1128 and 1132.

Prime Factorization of 1128

Prime factors of 1128 are 2, 3, 47. Prime factorization of 1128 in exponential form is:

1128 = 23 × 31 × 471

Prime Factorization of 1132

Prime factors of 1132 are 2, 283. Prime factorization of 1132 in exponential form is:

1132 = 22 × 2831

Now multiplying the highest exponent prime factors to calculate the LCM of 1128 and 1132.

LCM(1128,1132) = 23 × 31 × 471 × 2831
LCM(1128,1132) = 319224