text: # Find the least number which when divided by 35, 56 and 91 leaves the same remainder
  
  Question:
  
  Find the least number which when divided by 35, 56 and 91 leaves the same remainder 7 in each case.
  
  Solution:
  
  Least number which can be divided by 35, 56 and 91 is LCM of 35, 56 and 91.
  
  Prime factorization of 35, 56 and 91 is:
  
  35 = 5 × 7
  
  $56=2^{3} \times 7$
  
  91 = 7 × 13
  
  LCM = product of greatest power of each prime factor involved in the numbers $=2^{3} \times 5 \times 7 \times 13=3640$
  
  Least number which can be divided by 35, 56 and 91 is 3640.
  
  Least number which when divided by 35, 56 and 91 leaves the same remainder 7 is 3640 + 7 = 3647.
  
  Thus, the required number is 3647.