The product of two co-prime integers is 117. Their L.C.M must be__________?
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Answer: B. 117
Explanation
Co-prime integers share no common positive factors other than the number one. The highest common factor of any two distinct co-prime numbers is always one. The product of any two co-prime integers directly equals their least common multiple. Co-prime numbers are also known as relatively prime or mutually prime integers. The fundamental theorem of arithmetic governs the prime factorization of integers. For any two positive integers a and b, the product equals HCF multiplied by LCM.
Number theory principles underpin modern cryptography and secure data transmission algorithms. Simplifying fractions relies heavily on identifying co-prime numerator and denominator pairs. Modular arithmetic applications frequently utilize properties of co-prime integers. Choosing one represents only the highest common factor rather than the least common multiple. Choosing equality with the HCF contradicts the standard arithmetic product rule entirely. Choosing uncalculatable ignores the direct algebraic relationship between product and LCM.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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