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What is the Least Common Multiple of 2130 and 2138?

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 2130 and 2138 is 2276970.

LCM(2130,2138) = 2276970

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Least Common Multiple of 2130 and 2138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2130 and 2138, than apply into the LCM equation.

GCF(2130,2138) = 2
LCM(2130,2138) = ( 2130 × 2138) / 2
LCM(2130,2138) = 4553940 / 2
LCM(2130,2138) = 2276970

Least Common Multiple (LCM) of 2130 and 2138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2130 and 2138. First we will calculate the prime factors of 2130 and 2138.

Prime Factorization of 2130

Prime factors of 2130 are 2, 3, 5, 71. Prime factorization of 2130 in exponential form is:

2130 = 21 × 31 × 51 × 711

Prime Factorization of 2138

Prime factors of 2138 are 2, 1069. Prime factorization of 2138 in exponential form is:

2138 = 21 × 10691

Now multiplying the highest exponent prime factors to calculate the LCM of 2130 and 2138.

LCM(2130,2138) = 21 × 31 × 51 × 711 × 10691
LCM(2130,2138) = 2276970