Question

9. Find the smallest number which when divided by 15,20,25 and 30 leaves 5 as remainder in each case. Solve with solution
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Answer 1

LCM of 15,20,25,30=300

Now , 300 +5 =305

So, 15÷305

Remainder =5

20÷305

Remainder =5

25÷305

Remainder =5

30÷305

Remainder =5

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Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer is 35

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ When 15,20,25,30 is divided by a number the remainder is 5

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ The Number?

$\rule{110}1$

$\huge\sf\purple{Steps}$

So here first we have to take the LCM of 15,20,25,30

HCF(15,20,26)

➝ 15 = 5×3

➝ 20 = 2×2×5 = 2²×5

➝ 25 = 5×5 = 5²

➝ 30 = 5×2×3

So the HCF is the product of the least power of the common factors,that is here,

➢ HCF(15,2926) = 2×5×3

➢ $\sf\red{HCF = 30}$

So now if we need a reminder 5 we have to add 5 to the HCF,that is 30+5 = 35

Verification

➳ $\sf\dfrac{35}{15} = 5$

➳ $\sf\dfrac{35}{20} = 5$

➳ $\sf\dfrac{35}{25} = 5$

➳ $\sf\dfrac{35}{30} = 5$

$\rule{170}3$