Question

Find the smallest number which when added to 5 is exactly divisible by 12,14,18

Answer 1

Smallest number is 247

Given:

A Number added to 5 is exactly divisible by 12, 14 and 18

To find:

Smallest number when it is added to five which is exactly divisible by 12, 14 and 18

Solution:

To find the smallest number to add to 5 so that the number is exactly divisible by 12, 14 and 18

To find that number first let us find the LCM of 12, 14, 18,  

For 12 we get 2, 2, and 3

For 14 we get 2, 7

For 18 we get the factors 2, 3, 3

Now the LCM of above 3 numbers is 2, 2, 3, 3, 7 = 252

To find the smallest number we subtract the number 5 from 252, the number denotes the least number that is divisible by 12, 14, 18 is  

(252 – 5 = 247). If 5 are added to 247 then the number formed after addition is divided by 12, 14, and 18

Answer 2

Answer:

Required number = 247

Step-by-step explanation:

Find LCM of 12,14,18

2|12,14,18

____________

3| 6, 7, 9

____________

** 2, 7, 3

LCM(12,14,18) = 2×3×2×7×3

= 252

Now,

The least smallest number which when added to 5 is exactly divisible by 12,14,18

= LCM( 12,14,18 )- 5

= 252 - 5

= 247

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