Question

o find the least number which when divided by 506 and 759
leaves a remainder 12 in each case​

Answer 1

Step-by-step explanation:

Least required number is LCM (6,7,8,9,12 ) +1 6 =2*3 7 =7 8=2*2*2 9=3*3 12 =2*2*3

Answer 2

Answer:

The solution is simple. I add some explanation just for better understanding.

Let the number be x . Since x leaves remainder 1 when divided by 6,7,8,9 and 12, x can be written as

x=6a+1=7b+1=8c+1=9d+1=12e+1 for integers a,b,c,d and e .

Therefore,

x−1=6a=7b=8c=9d=12e.

This mean x−1 is common multiple of 6,7,8,9 and 12 . The least common multiple of 6,7,8,9 and 12 is the least value of x−1 which is 504 . The other multiples are 1008 , 1512 etc. Accordingly, the least value of x is 505. The other values are 1009,1513 etc.