Question

The smallest number which when divided by 30, 45, 75 and 60 leaves a remainder of 21, 36, 66 and 51 respectively is

Answer 1

Step-by-step explanation:

Given  

The smallest number which when divided by 30, 45, 75 and 60 leaves a remainder of 21, 36, 66 and 51 respectively is

• Given the number when divided by 30,45,75 and 60 will give a remainder 21,36,66 and 51.
• We need to find the required number , so subtracting the numbers we get
• 30 – 21 = 9, 45 – 36 = 9, 75 – 66 = 9, 60 – 51 = 9
• So the number is 9.
• Now we need to find the L.C.M of the divisors, so  
• 5   30   45   75   60
• 3    6     9     15   12
• 2    2     3      5     4
•      1     3      5     2
• So the factors are 5 x 3 x 2 x 1 x 3 x 5 x 2  
•                                 = 30 x 30
•                                  = 900
• Now the smallest number will be 9 less than 900 = 900 – 9
•                                                                                  = 891

Therefore the smallest number is 891.

Reference link

https://brainly.in/question/14146699