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17 Jun 2023, 00:01
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Shivank thought of the least number x which when divided by 12, 15 20 & 21 gave a remainder 10 in each case and x
is a multiple of 11. Shivank added a least number y to make x a perfect square. Find y?
is a multiple of 11. Shivank added a least number y to make x a perfect square. Find y?
Given: Shivank thought of the least number x which when divided by 12, 15 20 & 21 gave a remainder 10 in each case and x
is a multiple of 11. Shivank added a least number y to make x a perfect square.
Asked: Find y?
x = LCM(12,15,20,21)k + 10
LCM(3*2^2,3*5,2^2*5,3*7) = 2^2*3*5*7 = 420
x = 420k+ 10 = {430,850,1270,1690,2110,2530,....}
Since x is also a multiple of 11
x = 2530 = 2*5*11*23
\(\sqrt{x} = 50.299\)
Nearest perfect square = 51ˆ2 = 2601
y = 2601 - 2530 = 71
is a multiple of 11. Shivank added a least number y to make x a perfect square.
Asked: Find y?
x = LCM(12,15,20,21)k + 10
LCM(3*2^2,3*5,2^2*5,3*7) = 2^2*3*5*7 = 420
x = 420k+ 10 = {430,850,1270,1690,2110,2530,....}
Since x is also a multiple of 11
x = 2530 = 2*5*11*23
\(\sqrt{x} = 50.299\)
Nearest perfect square = 51ˆ2 = 2601
y = 2601 - 2530 = 71
