Two numbers are in the ratio of 5:7. If their LCM is 105, what is the…
2023
Two numbers are in the ratio of 5:7. If their LCM is 105, what is the difference between their squares ?
- A.
216
- B.
210
- C.
72
- D.
840
Attempted by 21 students.
Show answer & explanation
Correct answer: A
Answer:
216
Explanation:
Let h be the HCF. Then the two numbers are 5h and 7h.
Use Product = LCM × HCF: (5h)(7h) = 105·h ⇒ 35h^2 = 105h ⇒ h = 3.
Compute the difference of squares using (a^2 − b^2) = (a − b)(a + b):
Here, (7h)^2 − (5h)^2 = (7h − 5h)(7h + 5h) = (2h)(12h) = 24h^2.
Substitute h = 3: 24·h^2 = 24·9 = 216. (Alternatively, numbers are 15 and 21, and 21^2 − 15^2 = 441 − 225 = 216.)