Question

find the least no. that when divided by 16,18,20 leaves a remainder 4 in each case, but is completely divisible by 7

Answer 1

Solution :

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Given :

To Find the least number that when divided by 16,18,20 leaves a remainder 4 in each case, but is completely divisible by 7 .

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We can find the number by finding LCM for 16, 18, 20 and adding 4 to the LCM,. Then, checking divisiblity by with 7.

It is as follows :

⇒ LCM {16,18,20} = 720

⇒ 720 + 4 = 724,-> not divisible by 7

The closest number divisible by 7 = 721

⇒ 721 = (720 + 1) (The remainder = 1)

Multiplying it by 4,

We get,

⇒ (720 + 1) x 4

⇒ 2880 + 4

⇒ 2884 -> Divisible by 7

   ∴ The least number that when divided by 16,18,20 leaves a remainder 4 in each case, but is completely divisible by 7  is 2884,.
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