Two numbers have a product of 2025 and an HCF of 15. What is their LCM____________?
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Answer: C. 135
Explanation
The fundamental property states that the product of two numbers equals the product of their HCF and LCM. Dividing the given number product of twenty zero twenty five by the HCF of fifteen gives the LCM. Executing the division twenty zero twenty five divided by fifteen results in exactly one thirty five. The highest common factor represents the largest positive integer that divides evenly into both numbers. The least common multiple is the smallest positive integer divisible by both given numbers. Number theory guarantees that product equals HCF multiplied by LCM for any integer pair.
Cryptographic algorithms utilize common factor relationships to secure digital communication channels. Engineering gear ratios rely on least common multiples to synchronize rotating mechanical components. Arithmetic problem solving often uses divisibility properties to simplify complex algebraic relations. Option a is too large and fails the fundamental product relationship test. Option b represents an arithmetic calculation error during the division process. Option d results from incorrectly dividing by a different common factor value.
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- Mathematics
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- Mathematics
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- Difficulty
- medium
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