The H.C.F of 3240, 3600 and a third integer is 36, and their L.C.M is 24 * 35 * 52 * 72. Find the third number___________?
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Answer: A. 22 * 35 * 72
Explanation
The highest common factor divides evenly into all given integers, providing the baseline common prime factors. The least common multiple contains the highest exponents of all prime factors present across the integer set. Comparing prime factorizations allows the missing third integer components to be reconstructed accurately. Number theory relates the product of two numbers to the product of their greatest common divisor and least common multiple. Prime factorization breaks composite integers down into their foundational exponent components for analysis. LCM and HCF constraints restrict the possible prime factor combinations for unknown numbers in a set.
Cryptographic systems use advanced prime factorization principles to secure digital communication protocols. Algebraic simplification routines apply HCF and LCM calculations to reduce complex rational expressions. Computer algorithms compute greatest common divisors efficiently using Euclidean methods for data processing. Option B features incorrect prime exponents that fail to satisfy the specified least common multiple. Option C includes an altered base prime factor that violates the established highest common factor constraint. Option D miscalculates the required exponent for the primary factor terms in the third integer.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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