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What is the Least Common Multiple of 2050 and 2054?

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 2050 and 2054 is 2105350.

LCM(2050,2054) = 2105350

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Least Common Multiple of 2050 and 2054 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2050 and 2054, than apply into the LCM equation.

GCF(2050,2054) = 2
LCM(2050,2054) = ( 2050 × 2054) / 2
LCM(2050,2054) = 4210700 / 2
LCM(2050,2054) = 2105350

Least Common Multiple (LCM) of 2050 and 2054 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2050 and 2054. First we will calculate the prime factors of 2050 and 2054.

Prime Factorization of 2050

Prime factors of 2050 are 2, 5, 41. Prime factorization of 2050 in exponential form is:

2050 = 21 × 52 × 411

Prime Factorization of 2054

Prime factors of 2054 are 2, 13, 79. Prime factorization of 2054 in exponential form is:

2054 = 21 × 131 × 791

Now multiplying the highest exponent prime factors to calculate the LCM of 2050 and 2054.

LCM(2050,2054) = 21 × 52 × 411 × 131 × 791
LCM(2050,2054) = 2105350