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What is the Least Common Multiple of 7410 and 7420?

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 7410 and 7420 is 5498220.

LCM(7410,7420) = 5498220

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Least Common Multiple of 7410 and 7420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7410 and 7420, than apply into the LCM equation.

GCF(7410,7420) = 10
LCM(7410,7420) = ( 7410 × 7420) / 10
LCM(7410,7420) = 54982200 / 10
LCM(7410,7420) = 5498220

Least Common Multiple (LCM) of 7410 and 7420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7410 and 7420. First we will calculate the prime factors of 7410 and 7420.

Prime Factorization of 7410

Prime factors of 7410 are 2, 3, 5, 13, 19. Prime factorization of 7410 in exponential form is:

7410 = 21 × 31 × 51 × 131 × 191

Prime Factorization of 7420

Prime factors of 7420 are 2, 5, 7, 53. Prime factorization of 7420 in exponential form is:

7420 = 22 × 51 × 71 × 531

Now multiplying the highest exponent prime factors to calculate the LCM of 7410 and 7420.

LCM(7410,7420) = 22 × 31 × 51 × 131 × 191 × 71 × 531
LCM(7410,7420) = 5498220