15. Let L be the least common multiple of 173 and 105. Among all of t mon divisors > 1 of 175 and 105, Ict D bc the smallest. Which is correct of t Jowi A) D = 5 and 1050 B) D — 7 and L — 525 C) D = 5 and L = 525 D) D — 7 and L — 1050
Question
- Let L be the least common multiple of 173 and 105. Among all of t mon divisors > 1 of 175 and 105, Ict D bc the smallest. Which is correct of t Jowi A) D = 5 and 1050 B) D — 7 and L — 525 C) D = 5 and L = 525 D) D — 7 and L — 1050
Solution
First, let's find the least common multiple (LCM) of 173 and 105. The LCM is the smallest number that is a multiple of both numbers.
Since 173 is a prime number and does not divide 105, the LCM of 173 and 105 is simply their product, which is 18285.
Next, let's find the greatest common divisor (GCD) of 175 and 105. The GCD is the largest number that divides both numbers.
The prime factorization of 175 is 5^2 * 7 and of 105 is 5 * 7^2. The GCD is the product of the smallest power of each prime number that appears in both factorizations, which is 5 * 7 = 35.
So, none of the options A, B, C, D is correct. The correct answer should be D = 35 and L = 18285.
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