What is the highest four digit perfect square number divisible by 12 18 30?

Question 19 Exercise 6.3

Answer:

Solution:

L.C.M. of 8, 15 and 20 is 120.

Prime factors of 120 = 2 x 2 x 2 x 3 x 5

Here, prime factors 2, 3 and 5 have no pair. Therefore 120 must be multiplied by 2 x 3 x 5 to make it a perfect square.

\therefore120\times2\times3\times5=3600

Hence, the smallest square number which is divisible by 8, 15 and 20 is 3600.

Video transcript

hello kids welcome to Lido Homework in this video we're going to solve this A question which says to find the smallest square number that is divisible by each of the numbers 8 15 and 20. so to find the smallest square number Divisible by 8 15 and 20 Let's find out the lcm of the given numbers 8 15 and 20. okay so let's write that down 8 15 20. two fours are eight-fifteen two tens are two twos are four fifteen as it is two fives are ten two ones are two fifteen and five as it is the next number would be three three fives are fifteen and five as it is and the next number would be five okay so the lcm is 2 into 2 into 2 into 3 into 5 this is 8 into 3 into 5 which will give you 120 so the lcm of 8 15 and 20 is 120. Now pay attention to the word square that's mentioned over here you're just not finding any smallest number that not the smallest number that is there but you find the smallest square number so for that we need to figure out if 120 is a perfect square or not so for that we'll have to check it with prime factorization let's prime factorize 120 two six are zero two threes are two are two fives are three fives are and five ones Okay, so the factors in the prime factors of 120 are 2 into 2 into 2 into 3 into 5. so when you have to find a perfect square we first group the numbers and see how many numbers don't have a group and we multiply by those numbers right so you can see here 2 has a group great now this 2 is single 3 is single and 5 is single they don't have a group so what i have to do is I'll have to multiply 120 by one more two one more three and one more five so what What I'm doing is I'm going to add one more two here, one more three here. and another five here so that i get complete groups right and then the number that i get would be a perfect square so 120 into 2 into 3 into 5 will give me 3 6 double 0. so the smallest the square number that is divisible by 8 15 and 20 is six hundred i hope i was able to uh solve your doubt with this particular video please feel free to like to share and comment and I'll see you in another video Thank you.

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