find the least number of five digit which on dividing by 10,12,16,20,25 and 30 leaves remainder 8 in each case.
Answers
How will you find the least number of 5 digits that when divided by 12, 16, 20, and 25, leaves a remainder 8 in each case?
Break the problem down into steps:
Find the smallest number that will divide by these numbers leaving a remainder of zero. That’s the LCM (lowest common multiple). You can look up the method for calculating the LCM or you can find many LCM calculators on the internet.
The LCM of those numbers is 1200. That’s the smallest number that will divide by the given values.
But we need a 5 digit number so we need the smallest 5 digit number that is a multiple of 1200. Eight of them gives you 9600 which is still 4 digits but nine of them gives you 10800 so that’s the smallest 5-digit number that divides by the original values giving a remainder of zero.
But we need a remainder of 8. So, we simply add 8 to this result giving the final answer of 10808.
Hope it helps you ☺️
Step-by-step explanation:
Find the least number of five digits which on dividing by 10, 12, 16, 20, 25 and 30 leaves remainder 8 in each case.