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What is the Least Common Multiple of 3400 and 3413?

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 3400 and 3413 is 11604200.

LCM(3400,3413) = 11604200

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Least Common Multiple of 3400 and 3413 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3400 and 3413, than apply into the LCM equation.

GCF(3400,3413) = 1
LCM(3400,3413) = ( 3400 × 3413) / 1
LCM(3400,3413) = 11604200 / 1
LCM(3400,3413) = 11604200

Least Common Multiple (LCM) of 3400 and 3413 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3400 and 3413. First we will calculate the prime factors of 3400 and 3413.

Prime Factorization of 3400

Prime factors of 3400 are 2, 5, 17. Prime factorization of 3400 in exponential form is:

3400 = 23 × 52 × 171

Prime Factorization of 3413

Prime factors of 3413 are 3413. Prime factorization of 3413 in exponential form is:

3413 = 34131

Now multiplying the highest exponent prime factors to calculate the LCM of 3400 and 3413.

LCM(3400,3413) = 23 × 52 × 171 × 34131
LCM(3400,3413) = 11604200