Multiple choice

HCF of two numbers is 15 and their LCM is 180. If their sum is 105, then the numbers are-

  1. 30, 75

  2. 40, 65

  3. 35, 70

  4. 45, 60
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let numbers be 15a and 15b (since HCF=15). Then LCM = 15ab = 180, so ab = 12. Also 15a + 15b = 105, so a + b = 7. Factor pairs of 12: (1,12)→sum13, (2,6)→sum8, (3,4)→sum7. So a=3, b=4. Numbers are 15×3=45 and 15×4=60. Sum=105, HCF=15, LCM=180. Option D is correct.

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