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What is the Least Common Multiple of 2123 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 2123 and 2138 is 4538974.

LCM(2123,2138) = 4538974

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Least Common Multiple of 2123 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 2123 and 2138, than apply into the LCM equation.

GCF(2123,2138) = 1
LCM(2123,2138) = ( 2123 × 2138) / 1
LCM(2123,2138) = 4538974 / 1
LCM(2123,2138) = 4538974

Least Common Multiple (LCM) of 2123 and 2138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2123 and 2138. First we will calculate the prime factors of 2123 and 2138.

Prime Factorization of 2123

Prime factors of 2123 are 11, 193. Prime factorization of 2123 in exponential form is:

2123 = 111 × 1931

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 2123 and 2138.

LCM(2123,2138) = 111 × 1931 × 21 × 10691
LCM(2123,2138) = 4538974