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What is the Least Common Multiple of 8034 and 8050?

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 8034 and 8050 is 32336850.

LCM(8034,8050) = 32336850

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Least Common Multiple of 8034 and 8050 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8034 and 8050, than apply into the LCM equation.

GCF(8034,8050) = 2
LCM(8034,8050) = ( 8034 × 8050) / 2
LCM(8034,8050) = 64673700 / 2
LCM(8034,8050) = 32336850

Least Common Multiple (LCM) of 8034 and 8050 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8034 and 8050. First we will calculate the prime factors of 8034 and 8050.

Prime Factorization of 8034

Prime factors of 8034 are 2, 3, 13, 103. Prime factorization of 8034 in exponential form is:

8034 = 21 × 31 × 131 × 1031

Prime Factorization of 8050

Prime factors of 8050 are 2, 5, 7, 23. Prime factorization of 8050 in exponential form is:

8050 = 21 × 52 × 71 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 8034 and 8050.

LCM(8034,8050) = 21 × 31 × 131 × 1031 × 52 × 71 × 231
LCM(8034,8050) = 32336850