Find the least perfect square number divisible by 12,20,25.
Answers
Step-by-step explanation:
L.C.M of 12,20 and 25=300
prime factors are 2×2×3×5×5=300,which is not a perfect square. To make it perfect square, we need to multiply 3 to 300 i.e, 3×300=900
therefore,900 is the least perfect square number
Given:
Three numbers with values 12, 20, and 25.
To Find:
The least perfect square number such that it is divisible by the three numbers mentioned above is?
Solution:
The given problem can be solved using the concepts of LCM.
1. The three given numbers are 12, 20, and 25.
2. The Least Common Multiple of a number is defined as the smallest value of the multiple that is a common multiple of all the multiples of the given numbers.
For example, the least common multiple of 2, 4, and 8 is 8.
3. The LCM of 12, 20, and 25 is 300. 300 is the least common multiple of 12, 20, and 25.
4. 300 can be also written as,
=> 300 = 2 x 2 x 3 x 5 x 5,
=> For a number to be a perfect square, each factor must be repeated an even number of times.
=> Factor 3 is repeated only once, Hence multiplying the number with 3 makes it a perfect square,
=> 300 x 3 = 900 (900 is the square root of 30).
5. Hence, 900 is the least square number that is divisible by 12, 20, and 25.
Therefore, 900 is the least perfect square number that is divisible by 12, 20, and 25.