Question

Find the smallest number which when reduced by 3 is divisible by 24, 36 and 40.​

Answer 1

Question :- Find the smallest number which when reduced by 3 is divisible by 24, 36 and 40. ?

Solution :-

in order to find the required number , first we will find the smallest number which is divisible by 24, 36 and 40.

we know that, to find the smallest number divisible by all given numbers we need to find the LCM of given numbers.

So,

To find LCM of 24, 36 and 40 , we find prime factors of them first and than multiply the factors with highest powers .

So,

Prime factors of 24, 36 and 40 are :-

→ 24 = 2 * 2 * 2 * 3 = 2³ * 3

→ 36 = 2 * 2 * 3 * 3 = 2² * 3²

→ 40 = 2 * 2 * 2 * 5 = 2³ * 5

LCM = 2³ * 3² * 5 = 8 * 9 * 5 = 360 .

Now, we have smallest number which is exactly divisible by 24, 36 and 40.

Therefore, we have to find the the number which when we reduced by 3 , we will get 360 .

Hence,

→ Required number = 360 + 3 = 363 (Ans.)

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Answer 2

HELLO DEAR,

GIVEN :- 24,36 and 40.

TO FIND :- The smallest number which when reduced( less) by 3 is divisible by 24,36 and 40.

SOLUTION:-

We have to first find the smallest number which is dibisible by 24 ्््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््््36 and 40 and then add 3 to that number to find answer.

Lets start,

The smallest divisible number be the LCM of 24,36 and 40.

24=2×2×2×3

36=2×2×3×3

40=2×2×2×5

______________

LCM= 2×2×2×3×3×5

=360.

So, the smallest number which is divisible by 24,36 and 40 is 360.

Therefore , the smallest number which is divisible by 24,36 and 40 when it is reduced by 3 is ,

360+ 3 = 363. ANSWER.

I HOPE IT'S HELP YOU DEAR,

THANKS.