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· 1 Months ago

q 116026 (Question: 116026.0 )

kindly explain how did you calculate square number using L C M ....its not clear

Question:

The least positive integer is a perfect square and is also divisible by 27, 39 and 48. What is the least positive integer?

Options:
A) 8112
B) 24336
C) 73008
D) 219024
Solution:
Ans:(d)

27=3 x 3 x 3

39 = 3 x 13

48 = 2 x 2 x 2 x 2 x 3

The least positive integer divisible by 27, 39 and 48 is the LCM of these numbers = 2 x 2 x 2 x 2 x  3 x 3 x 3 x 13 = 5116

Therefore, the required square number = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 13 x 3 x 13 = 219024

Knowledge Expert

· commented

· 1 Months ago

its easy na....square of a = axa = a^2...



27=3 x 3 x 3

39 = 3 x 13

48 = 2 x 2 x 2 x 2 x 3

The least positive integer divisible by 27, 39 and 48 is the LCM of these numbers = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 13 = 5116


Now, look at above factorization of 5116:

2 appears 4 times

3 appears 3 times

13 appears 1 times

these appearance should be even number times to be perfect square...



Therefore, the required square number = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 13 x 3 x 13 = 219024

now look:

2 appears 4 times

3 appears 4 times

13 appears 2 times


now its perfect square...
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