Find the largest possible positive integer that will divide 398, 436, and 542 leaving remainder 7, 11, 15 respectively.

Ans:  The  required number is the HCF of the numbers

  Find the HCF of 391, 425 and 527 by Euclid’s algorithm

  ∴ HCF (425, 391) = 17

  Now we have to find the HCF of 17 and 527
    527 = 17 х 31 +0 

  ∴ HCF (17,527) = 17
∴ HCF (391, 425 and 527) = 17

5. Find the least number that is divisible by all numbers between 1 and 10 (both inclusive).
  
(Ans:2520) Ans:  The required number is the LCM of 1,2,3,4,5,6,7,8,9,10

  ∴ LCM = 2  × 2 × 3 × 2 × 3 × 5 × 7  = 2520