Math, asked by Kuldeep2050, 4 months ago

Find a least number which when divided by 12 15 18 and 20 leaves a reminder 5 in each case.

Answers

Answered by Anonymous
28

Solution :-

Here, we have to find a least number so that which when divided by 12 , 15 , 18 and 20 leaves a remainder 5

Therefore,

LCM of 12 , 15 , 18 and 20

12 = 2 * 5 * 2.

15 = 3 * 5

18 = 3 * 3 * 2

20 = 2 * 2 * 5

LCM = 2 * 2 * 3 * 3 * 5 = 180

Therefore,

The least number is 180 + 5 = 185 .

Verification :-

1) 185/ 12

Here, Quotient = 15

Remainder = 5

2) 185/15

Quotient = 12

Remainder = 5

3) 185/18

Quotient = 10

Remainder = 5

4) 185/20

Quotient = 9

Remainder = 5

Hence, The least number is 185.

Answered by Ujjwal202
8

Question :-

  • Find a least number which when divided by 12 15 18 and 20 leaves a reminder 5 in each case.

Answer :-

  • The least number is 185.

Solution :-

  • Here, we have to find a least number so that which when divided by 12 , 15 , 18 and 20 leaves a remainder 5

  • so, we have to take the LCM

  • LCM of 12 , 15 , 18 and 20

  • 12 = 2 * 5 * 2.

  • 15 = 3 * 5

  • 18 = 3 * 3 * 2

  • 20 = 2 * 2 * 5

  • LCM = 2 * 2 * 3 * 3 * 5 = 180

Therefore,

  • The least number is 180 + 5 = 185

Verification

1) 185/ 12

  • Quotient = 15

  • Remainder = 5

2) 185/15

  • Quotient = 12

  • Remainder = 5

Verified

Hence,

  • The least number is 185.
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