Question

Find the greatest number of 4 digits which when divided by 10,11,15,22 leaves remaindre of 3,4,8,15

Answer 1

Firstly, we will subtract 3, 4, 8 and 15

10 - 3 = 7

11 - 4 = 7

15 - 8 = 7

22 - 15 = 7


We will find the prime factors of 10, 11, 15, 22

10 = 2 × 5

11 = 11

15 = 3 × 5

22 = 2 × 11


Now, we will find the LCM:

LCM = 2 × 3 × 5 × 11 = 330


Now, we will find the number

9999 ÷ 330 = 30

remainder 9

30 × 330 = 9900

9900 - 7 = 9893


$\therefore{}$ The number is 9893.

Answer 2

here is your answer


LCM(10,11,15,22)=330
GREATEST 4 DIGIT NO=9999
DIVISIBLE BY 330 WILL BE 9900
HERE 10-3=7,11-4=7,15-8=7,22-15=7
THUS 9900-7=9893

OK