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What is the Least Common Multiple of 7406 and 7413?

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 7406 and 7413 is 7842954.

LCM(7406,7413) = 7842954

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Least Common Multiple of 7406 and 7413 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7406 and 7413, than apply into the LCM equation.

GCF(7406,7413) = 7
LCM(7406,7413) = ( 7406 × 7413) / 7
LCM(7406,7413) = 54900678 / 7
LCM(7406,7413) = 7842954

Least Common Multiple (LCM) of 7406 and 7413 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7406 and 7413. First we will calculate the prime factors of 7406 and 7413.

Prime Factorization of 7406

Prime factors of 7406 are 2, 7, 23. Prime factorization of 7406 in exponential form is:

7406 = 21 × 71 × 232

Prime Factorization of 7413

Prime factors of 7413 are 3, 7, 353. Prime factorization of 7413 in exponential form is:

7413 = 31 × 71 × 3531

Now multiplying the highest exponent prime factors to calculate the LCM of 7406 and 7413.

LCM(7406,7413) = 21 × 71 × 232 × 31 × 3531
LCM(7406,7413) = 7842954