Question

6. Find the least number of 5-digits which is exactly divisible by 28, 49 and 14 after adding 9 to it.
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Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Prime Factorisation of 28,49, 14 :-

→ 28 = 2 * 2 * 7 = 2² * 7

→ 49 = 7 * 7 = 7²

→ 14 = 2 * 7

LCM = 2² * 7² = 4 * 49 = 196 .

Now, we have to find least number of 5-digits which is exactly divisible by 28, 49 and 14 after adding 9 to it.

So, we can conclude that,

→ The number will be in the form of = (196n - 9) .

And, Least five digit Number is = 10000 .

Lets see Factor of 196 near to 10000 which is also greater than 10000 .

→ 10000 = 196 * 51 + 4

So,

→ 196 * 52 = 10,192 .

10,192 is our Least 5 - digit number that satisfy the above condition..

But,

it has been said that when we add 9 we will get this result.

Therefore,

→ Our Required Number will be = 10,192 - 9 = 10,183 (Ans.)

Hence, 10,183 is the Required Least 5 digit Number..

Answer 2

$\sf{\underline{\underline{\red{Question:-}}}}$

Find the least number of 5-digits which is exactly divisible by 28, 49 and 14 after adding 9 to it.

$\sf{\underline{\underline{\red{On\:Prime\: Factorization:-}}}}$

we know least 5 digit number is 10000

$\sf→ 28= <u>2</u><u>×</u><u>2</u>×7\\\sf→ 49=<u>7</u><u>×</u><u>7</u>\\\sf→ 14=2×7\\\sf→ 2×2×7×7= 196$

Now,

we have to check factor of 196 nearest to 10000 and it will also greater than 10000

$\sf→ 10000= 196×51+4= 10192$

According to question:-

10192 is least 5 digit number by by the question we have to add 9 to get the finial result.

Therefore,

$\sf→ 10192-9= 10183 \: Answer$