Which is the greatest 3 digit number which when divided by 6 9 and 12?

Question 11 Exercise 3.7

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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