Question

find the largest four digit number which on being divided by a 6 10 15 leaves a remainder of 5 every time

Answer 1

9995

it is the right answer

Answer 2

Answer:

The largest four digit number which on being divided by a 6 10 15 leaves a remainder of 5 every time is 9995.

Step-by-step explanation:

• The largest four digit number is 9999.
• To know the largest four digit number which on being divided by a 6, 10 and 15 leaves a remainder of 5, we have to calculate the L.C.M. of 6,10 and 15.
• L.C.M. means least common multiples.
• Multiples of 6 = 6, 12, 18, 24, 30....
• Multiples of 10 = 10, 20, 30, 40, 50....
• Multiples of 15 = 15, 30, 45, 60, 75....
• least common multiples of 6, 10, 15 is 30.
• If we devide 30 with the greatest four digit number 9999 ,we get
• 9999÷ 30= quotient 333 and remainder 9.
• If we substract 9 from 9999, then there will be no remainder.
• So the greatest four digit number which is divisible by 30 is 9999-9= 9990.
• As 30 is divisible by 6,10 and 15, then 9990 is also divisible by 6,10,15.
• But to leave the remainder 5, the number will be 9990+5 =9995
• So 9995 is the greatest four digit which on divided by 6, 10 and 15, there will be remainder 5 in each case.

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