find the greatest no of 5 digits which on dividing by 10,12,16,20 and

1.	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» t we need to find the LCM 10,12,16,20,24 LCM of 10,12,16,20,24 $2 \underline{ \|10.12.16.20.24} \\ 2 \underline{\| \: 5. \: \: <klux>6</klux>. \: \: 8. \: 10. \: 12 } \\ 2 \underline{ \| \: 5. \: \: 3. \: \: 4. \: \: \: 5. \: 6 \: } \\5 \| \underline{5 \: \: .3. \: \: 2. \ \: 5. \: \: 3} \\ \: 1. \: \: 3. \: \: 2. \: \: 1 \: \: 3 \\ \\ \sf \: lcm = 2 \times 2 \times 2 \times 5 \times 3 \times 2 \times 3 = 720$ 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

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»

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

LCM of 10,12,16,20,24

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

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

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