Question

find the greatest no of 5 digits which on dividing by 10,12,16,20 and 24 leaves in each case 3 as remainder​

Answer 1

first we need to find the LCM 10,12,16,20,24

LCM of 10,12,16,20,24

$2 \underline{ |10.12.16.20.24} \\ 2 \underline{| \: 5. \: \: 6. \: \: 8. \: 10. \: 12 } \\ 2 \underline{ | \: 5. \: \: 3. \: \: 4. \: \: \: 5. \: 6 \: } \\5 | \underline{5 \: \: .3. \: \: 2. \ \: 5. \: \: 3} \\ \: 1. \: \: 3. \: \: 2. \: \: 1 \: \: 3 \\ \\ \sf \: lcm = 2 \times 2 \times 2 \times 5 \times 3 \times 2 \times 3 = 720$

• We have the greatest five digit number : 99999

$\sf \: Now \: . \: \dfrac{ 99999}{720}= 130 \: remainder \: will \: be \: \pink{ 639}$

• → The required number = ( 99999-639 ) + 6 = 99366

Answer 2

Step-by-step explanation:

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