The greatest perfect square less than 20000 which is divisible by each of 2,5,7

Question

The greatest perfect square less than 20000 which is divisible by each of 2,5,7 and 8 is :___

Answer:
:
The least number that is exactly divisible by 2, 5, 7 and 8 is its LCM which is 280.
Since 280 is not a perfect square, the multiples of 280 are checked for perfect square.
Now,

280 = 2^{3} \times 5^{1} \times 7^{1}

. So, 280 must be multiplied with a minimum of

2^{1} \times 5^{1} \times 7^{1}

i.e. 70 to make it a perfect square.
So, the required number is:

280 \times 70 = 19600

which is the greatest perfect square less than 20000 satisfying this condition.

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. An eight digit number divisible by 9 is to be formed by using 8 digits out of the digits 0,1,2,3,4,5,6,7,8,9 withou....without replacement. The number of ways in which can be done is

Question 2. Suppose f(x)=(x+1)2 for x≥1. If g(x) is the function whose graph is reflection of the graph of f(....f(x) with respect to the line y = x, then g(x) equals:

Question 3. An engine without wagon can go at the rate of 24 kmph and its speed diminishes by a quantity which vari....number of wagons with which the wagon can move is :

Question 4. In a class, there are 100 students. They are asked to vote for the teachers they like among five teachers namely Vanita ....voted for a minimum of two of the five teachers.

Question 5. Find the remainder when 4001000 is divided by 17?....

Question 6. In the given equilateral triangle, the smaller circle and the bigger semi circle are inscribed inside. What is the value....circle are inscribed inside. What is the value of XY

Question 7. If 2g(x)+3g(1x)=x−1, then find the value of g(2).....

Question 8. If f(x)=xx+1, determine the value of g(2) if, g(x)=f[1x+1]−1f(x+1).....

Question 9. Let y=12+13+12+13+..... What is the value of y?....

Question 10. Let g(x)= |x+1|. The number of values that 'x' can take (given that its range is between -2 & +....inclusive) for which g(x-3), g(x-1), g(x+1) are in AP is?

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0

Submit Solution

More Questions on This Topic :

Latest Videos

Latest Test Papers