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What is the Least Common Multiple of 12200 and 12208?

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 12200 and 12208 is 18617200.

LCM(12200,12208) = 18617200

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Least Common Multiple of 12200 and 12208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12200 and 12208, than apply into the LCM equation.

GCF(12200,12208) = 8
LCM(12200,12208) = ( 12200 × 12208) / 8
LCM(12200,12208) = 148937600 / 8
LCM(12200,12208) = 18617200

Least Common Multiple (LCM) of 12200 and 12208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12200 and 12208. First we will calculate the prime factors of 12200 and 12208.

Prime Factorization of 12200

Prime factors of 12200 are 2, 5, 61. Prime factorization of 12200 in exponential form is:

12200 = 23 × 52 × 611

Prime Factorization of 12208

Prime factors of 12208 are 2, 7, 109. Prime factorization of 12208 in exponential form is:

12208 = 24 × 71 × 1091

Now multiplying the highest exponent prime factors to calculate the LCM of 12200 and 12208.

LCM(12200,12208) = 24 × 52 × 611 × 71 × 1091
LCM(12200,12208) = 18617200