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What is the Least Common Multiple of 1102 and 1122?

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 1102 and 1122 is 618222.

LCM(1102,1122) = 618222

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Least Common Multiple of 1102 and 1122 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1102 and 1122, than apply into the LCM equation.

GCF(1102,1122) = 2
LCM(1102,1122) = ( 1102 × 1122) / 2
LCM(1102,1122) = 1236444 / 2
LCM(1102,1122) = 618222

Least Common Multiple (LCM) of 1102 and 1122 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1102 and 1122. First we will calculate the prime factors of 1102 and 1122.

Prime Factorization of 1102

Prime factors of 1102 are 2, 19, 29. Prime factorization of 1102 in exponential form is:

1102 = 21 × 191 × 291

Prime Factorization of 1122

Prime factors of 1122 are 2, 3, 11, 17. Prime factorization of 1122 in exponential form is:

1122 = 21 × 31 × 111 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 1102 and 1122.

LCM(1102,1122) = 21 × 191 × 291 × 31 × 111 × 171
LCM(1102,1122) = 618222