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What is the Least Common Multiple of 2101 and 2117?

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 2101 and 2117 is 4447817.

LCM(2101,2117) = 4447817

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Least Common Multiple of 2101 and 2117 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2101 and 2117, than apply into the LCM equation.

GCF(2101,2117) = 1
LCM(2101,2117) = ( 2101 × 2117) / 1
LCM(2101,2117) = 4447817 / 1
LCM(2101,2117) = 4447817

Least Common Multiple (LCM) of 2101 and 2117 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2101 and 2117. First we will calculate the prime factors of 2101 and 2117.

Prime Factorization of 2101

Prime factors of 2101 are 11, 191. Prime factorization of 2101 in exponential form is:

2101 = 111 × 1911

Prime Factorization of 2117

Prime factors of 2117 are 29, 73. Prime factorization of 2117 in exponential form is:

2117 = 291 × 731

Now multiplying the highest exponent prime factors to calculate the LCM of 2101 and 2117.

LCM(2101,2117) = 111 × 1911 × 291 × 731
LCM(2101,2117) = 4447817