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What is the Least Common Multiple of 5405 and 5420?

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 5405 and 5420 is 5859020.

LCM(5405,5420) = 5859020

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Least Common Multiple of 5405 and 5420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5405 and 5420, than apply into the LCM equation.

GCF(5405,5420) = 5
LCM(5405,5420) = ( 5405 × 5420) / 5
LCM(5405,5420) = 29295100 / 5
LCM(5405,5420) = 5859020

Least Common Multiple (LCM) of 5405 and 5420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5405 and 5420. First we will calculate the prime factors of 5405 and 5420.

Prime Factorization of 5405

Prime factors of 5405 are 5, 23, 47. Prime factorization of 5405 in exponential form is:

5405 = 51 × 231 × 471

Prime Factorization of 5420

Prime factors of 5420 are 2, 5, 271. Prime factorization of 5420 in exponential form is:

5420 = 22 × 51 × 2711

Now multiplying the highest exponent prime factors to calculate the LCM of 5405 and 5420.

LCM(5405,5420) = 51 × 231 × 471 × 22 × 2711
LCM(5405,5420) = 5859020