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What is the Least Common Multiple of 6414 and 6420?

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 6414 and 6420 is 6862980.

LCM(6414,6420) = 6862980

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Least Common Multiple of 6414 and 6420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6414 and 6420, than apply into the LCM equation.

GCF(6414,6420) = 6
LCM(6414,6420) = ( 6414 × 6420) / 6
LCM(6414,6420) = 41177880 / 6
LCM(6414,6420) = 6862980

Least Common Multiple (LCM) of 6414 and 6420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6414 and 6420. First we will calculate the prime factors of 6414 and 6420.

Prime Factorization of 6414

Prime factors of 6414 are 2, 3, 1069. Prime factorization of 6414 in exponential form is:

6414 = 21 × 31 × 10691

Prime Factorization of 6420

Prime factors of 6420 are 2, 3, 5, 107. Prime factorization of 6420 in exponential form is:

6420 = 22 × 31 × 51 × 1071

Now multiplying the highest exponent prime factors to calculate the LCM of 6414 and 6420.

LCM(6414,6420) = 22 × 31 × 10691 × 51 × 1071
LCM(6414,6420) = 6862980