What is the smallest number which is divisible of divisible by 8 and 12?

Question 11 Exercise 3.7

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Answer:

SOLUTION:

Firstly, we need to find out the LCM of 8,10,12.

\operatorname{lcm}\ of\ 8,10\ and\ 12\ =\ 2\times2\times2\times3\times5=120

greatest 3 digit number =999

ART

(greatest 3 digit number - remainder)

999-39=960

Video transcript

Welcome to lido homework today. We're in question number 5, which determines the greatest three-digit number exactly divisible by 8 10 and 12 losses. The first the very first step is to find the LCM of these numbers. All right, so I think we all know the method of finding LCM, you put three columns like this for three numbers. Okay. We'll do it using a ruler. No just a second. Alright, so we put three columns one. Two And three right and then you have to do the prime factorization of these three numbers together. All right, so let's begin. So first is 8 10 and 12. Now go ahead. And first of all find the smallest prime number prime number which divides all of them equally. So this first one that will come to Mi is to write so we divide by 2. What will be left is four five and six? Right again, you'll go with two then you'll have two five and six 3s. So whatever is left to right as it is. Okay, so then again to this will become 1 this will remain 5 and this three takedown then take three. All right, if you take 3 this will become 1 this will remain 5 and this will become one again or take five now so 5 and this will become 1 1 1 so that's the end and the lcms when you multiply all of them so 2 into 2. 2 into 3 into 5 gives you 120. Okay. So 120 is the LCM Next Step. What is the greatest three-digit number only the greatest three-digit number. Okay. The greatest three-digit number is 999 but what do we have to find? We have to find the greatest three-digit number which divides these numbers exactly the numbers 8 10 and 12 exactly. Now what you'll do is you'll divide 999 by the LCM of 8 10 and 12 which is 120. So let's go ahead and do it. The second just it is fair. Okay, let's go forward. So we have to divide 999. 999 With 120. So the nearest is 128 the which will give you 960. And so the remainder will come out to be 39. Alright, so your answer is the greatest three-digit number - this remainder will give you the smallest three digit number which is divisible by 8 and 12. Okay, the greatest three-digit number that is 999 - 39 is your answer. So 999 - 39 Is 960 so thus greatest three-digit number which divides 8 10 and 12 exactly is 960. Thank you so much guys, if you have any doubts, please happen in the comments and I'll do my best to get back to you. Please like the video and subscribe the channel. Thank you very much.

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Answer

Hint: The rule for divisibility by 6 is that the number should be divisible by 2 and 3. For 8, the rule is that the last three digits should be divisible by 8. For divisibility by 12, the number should be divisible by 3 and 4.

Complete step-by-step solution -

Solution:

We will be using the concept of LCM(Least Common Multiple) to solve this.

We know that the smallest 3-digit number is 100

Let's find the LCM of 6, 8, and 12 as shown below.

As we can observe from the division method, LCM of 6, 8, and 12 is 2 × 2 × 2 × 3 = 24

Thus, all the multiples of 24 will also be divisible by 6, 8, and 12.

Now we will divide the smallest-3 digit number with the LCM obtained, and the remainder will be subtracted from the dividend, and 24 will be added to it to make it perfectly divisible.

Let us observe below.

So, the smallest three digit multiple of 24 will be,

100 = (100 – 4) + 24 = 96 + 24 = 120

Hence, the smallest 3-digit number which is exactly divisible by 6, 8, and 12, is 120.

You can also use the LCM Calculator to solve this.

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 Question 4

Summary:

The smallest 3-digit number which is exactly divisible by 6, 8, and 12, is 120.

☛ Related Questions:

AcademicMathematicsNCERTClass 6

Given:

8, 10 and 12

To find:

We have to find the smallest 4-digit number divisible by 8, 10 and 12

Solution:

To find the smallest 4 digit number which is exactly divisible by 8, 10 and 12, we have to first find the LCM of 8, 10 and 12:

$8\ =\ 2\ \times \ 2\ \times \ 2$

$10\ =\ 2\ \times \ 5$

$12\ =\ 2\ \times \ 2\ \times \ 3$

LCM = 2 $\times $ 2 $\times $ 2 $\times $ 3 $\times $ 5 = 120

So, LCM of 8, 10 and 12 is 120. But we want the least 4 digit number, which is exactly divisible by 8, 10 and 12. 

Smallest 4 digit number = 1000.

Now,

$1000\ =\ ( 8\ \times \ 120) \ +\ 40$

Next higher quotient is 9.

So, the required number = 9 × 120 = 1080

Hence, the required number is 1080, which is exactly divisible by 8, 10 and 12.

Updated on 10-Oct-2022 10:11:41