The HCF and LCM of two positive integers are 18 and 360, respectively. If one…
2026
The HCF and LCM of two positive integers are 18 and 360, respectively. If one integer is 90, find the other integer.
Answer: B. 72 — ConceptFor any two positive integers a and b, a × b = HCF(a, b) × LCM(a, b). Therefore, if three of these four quantities are known, the fourth can be found…
- A.
45
- B.
72
- C.
100
- D.
5
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Show answer & explanation
Correct answer: B
Concept
For any two positive integers a and b, a × b = HCF(a, b) × LCM(a, b).
Therefore, if three of these four quantities are known, the fourth can be found by rearranging this identity.
Application
Let the unknown integer be x.
Substitute the given values: 90 × x = 18 × 360.
Divide both sides by 90: x = (18 × 360) ÷ 90.
Simplify: x = 18 × 4 = 72.
Cross-check
HCF(90, 72) = 18 and LCM(90, 72) = (90 × 72) ÷ 18 = 360, so both given conditions are satisfied.
Result
The other integer is 72.