find a perfect square which is divisible by 24,72,18
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find a perfect square which is divisible by 24,72,18
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the answer is 576... hope it helps
Answer:
The answers given are all correct.
8=23
12=22∗3
15=3∗5
20=22∗5
So choosing the maximum of all the prime exponents that exist in the numbers above, we have,
LCM = 23∗3∗5=120
Now, I will use an approach which others have not used to get to the least perfect square.
120 = 23∗3∗5
Now in a perfect square, ALWAYS, exponent of each prime is always even.
So, we will change the exponent of 2 from 3 to 4.
We will change the exponent of 3 from 1 to 2.
We will change the exponent of 5 from 1 to 2.
Finally we have the number 24∗32∗52=3600 .
So, required answer is 3600.
What is the least perfect square number which is exactly divisible by 12, 18 and 20?
What is the least number that is exactly divisible by 8, 9, 12, 15 and 18 and is also a perfect square?
What is the least number which is a perfect square and exactly divisible by 10, 12, and 15?
What is the least square number which is exactly divisible by 10, 12, 15 and 18?
What are the steps to find out the least number which is a perfect square and exactly divisible by 10, 12, and 15?
Find the LCM of given numbers. Square it to get the answer.
8 = 2^3
12 = 2^2 * 3
15 = 3 * 5
20 = 2^2 * 5
LCM = 2^3 * 3 * 5
= 120
Answer = LCM^2
= 14400
It is not given in the options.
Edit :
I made a mistake. Thank you for pointing it out .
The correct method would be
Find the LCM of the given numbers(which is 120 in this case)
Find the prime factorisation of the LCM
(120 = 2^3 *3 *5)
Now multiply the LCM by prime factors so that all the prime factors will have even multiplicities.
Answer = (2^3 * 3* 5) * (2*3*5)
= 2^4 * 3^2 * 5^2
= 3600
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