Answer:
The smallest number which when divided by 8,12,15,18 and 24 leaves 3 as remainder is 363.
Explanation:
To get the smallest number which when divided by 8,12,15,18 and 24 leaves 3 as remainder, we need to find the Least Common Multiple(LCM) of 8,12,15,18 and 24. The least common multiple is the number which is divisible by all the numbers 8,12,15,18 and 24 (that is it leaves 0 as a remainder).
After finding the Least Common Multiple(LCM) we will add 3 to the LCM value. This value will be the smallest number which when divided by 8,12,15,18 and 24 leaves 3 as remainder.
So, let's find the LCM:
LCM is 2 x 2 x 3 x 2 x 5 x 3 = 360
The LCM we got is 360.
Now add 3 to get the resultant answer: 360 + 3
Answer is 363
Let's verify the answer:
363/8 gives quotient as 45 and remainder as 3.
363/12 gives quotient as 30 and remainder as 3.
363/15 gives quotient as 24 and remainder as 3.
363/18 gives quotient as 20 and remainder as 3.
Answer: 363