Find the least perfect square, which is divisible by each of 15, 20 and 36?
Answers
Answer:
Let us first find the LCM of 15, 20 and 36 using prime factorisation.
2 | 15, 20, 36
2 | 15, 10, 18
3 | 15, 5, 9
3 | 5, 5, 3
5 | 5, 5, 1
| 1, 1, 1
2 x 2 x 3 x 3 x 5 = 180
Making pairs of two numbers, we get (2x2) and (3x3) and 5 is unpaired. Hence, two make it a pair, we multiply the number by 5.
180 x 5
= 900
= 30^2
Answer:
30² is least perfect square which is divisible by each 15, 20 and 36 .
Step-by-step explanation:
We will start by taking the LCM of the given numbers:
5 | 15 20 36
3 | 3 4 12
3 | 1 4 6
2 | 1 4 2
2. | 1 2 1
| 1 1 1
LCM =180
hence , we see that
3 and 2 are in pairs . I,e: (2,2) and (3,3).
As 5 is not in pair ,
we have to multiply it with the LCM
=180×5
=900
=30².
therefore, 30² is least perfect square which is divisible by each 15, 20 and 36 .
(#SPJ2)