Question

3. Find the least number which when divided by 6, 15 and 18 leaves a remainder of 5 each time?​

Answer 1

$\huge{\tt{\fcolorbox{aqua}{azure}{\color{red}{Answer}}}}$

95 is the least number which when divided by 6, 15 and 18 leaves a remainder 5 in each case.

To find the least number which when divided by 6, 15 and 18 leaves a remainder 5 in each case we have to do the following steps:

Find the LCM of 6, 15 and 18

Add 5 in to the LCM

$\underline {\tt\pink{Explanation}}$

Below is the LCM shown for 6,15 and 18 using Prime Factorization

6 = 2 × 3

15 = 3 × 5

18 = 2 × 3 × 3

Thus, the LCM of 6,15 and 18 = 2 × 3 × 3 × 5 = 90

Now, adding 5 to 90, we get 90 + 5 = 95

$\underline {\tt\purple{VERIFICATION }}$

1) 95/6

Quotient = 15

Remainder = 5

2) 95/15

Quotient = 6

Remainder = 5

3) 95/18

Quotient = 5

Remainder = 5

Hence, 95 is the least number which when divided by 6, 15 and 18 leaves a remainder 5 in each case.

Answer 2

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• Given numbers are 6, 15 and 18

$\underline{\underline{\sf{\maltese\:\:To\: Find}}}$

• Number which when gets divided by 6, 15 and 18 leaves 5 as remainder.

$\underline{\underline{\sf{\maltese\:Concept \:Used}}}$

• The LCM of numbers 6, 15 and 18 leaves the remainder as 0, so we have to add 5 to the LCM of the given numbers to get the answer.

$\underline{\underline{\sf{\maltese\:Formula \:Used}}}$

LCM of two or more numbers = Product of the greatest power of each prime factor, involved in the numbers.

$\underline{\underline{\sf{\maltese\:Calculations \:}}}$

Lets find out the LCM of given numbers by prime factorization method.

➙Factors of 6 = 2 × 3

➙Factors of 15 = 3 × 5

➙Factors of 18 = 2 × 3 × 3

LCM of 6, 15 and 18 = Product of the greatest power of each prime factor, involved in the numbers.

⇒LCM of 6, 15 and 18 = 2 × 3² × 5

⇒LCM of 6, 15 and 18 = 2 × 3 × 3 × 5

⇒LCM of 6, 15 and 18 = 90

Number which when gets divided by 6, 15 and 18 leaves 5 as remainder = LCM + 5

Number which when gets divided by 6, 15 and 18 leaves 5 as remainder = 90 + 5 = 95.

Hence, 95 is the required number which when gets divided by 6, 15 and 18 leaves 5 as remainder.