10 grade maths> H.C.F of 3240,3600 and a third number is ...

H.C.F of 3240,3600 and a third number is 36 and their L.C.M is 2^4x3^5x5^2x7^2.Find the third number.

Smrithi Manoharan , 11 Years ago

Grade 10

4 Answers

Pallavi Das

Last Activity: 11 Years ago

H.C.F=36=2^2*3^2 L.C.M=2^4*3^5*5^2*7^2 3600=2^4*3^2*5^2 3240=2^2*3^4*5 Third no.= 2^2*3^2*7^2*3^3 =2^2*3^5*7^2

Aiman Saad Baig

Last Activity: 11 Years ago

HCF (3240, 3600, y) = 36 LCM (2^4x3^5x5^2x7^2) = 4846100 We know that; HCF X LCM = Product of the numbers 36 X 4846100 = 3240 X 3600 X y 174459600 = 11664000 X y y = 174459600 / 11664000 y = FIND OUT ?

Akash Singh

Last Activity: 7 Years ago

3600=2^4*3^2*5^23240=2^2*3^4*5H.C.F =36=2^2 *3^2Since H.C.F is the product of lowest power of common Factor , so the third Number must have (2^2 *3^2) as it`s factor .Since L.C.M is the Product of Highest power of Common Prime Factor , So the Third number must have 3^5 and 7^2 as it`s factor .Therefore , Third number =2^2*3^5*7^2

Kushagra Madhukar

Last Activity: 5 Years ago

Dear student,
Please find the attached solution to your problem below.

3600 = 2⁴*3²*5²
3240 = 2²*3⁴*5
H.C.F = 36 = 2²*3²
Since H.C.F is the product of lowest power of common Factor , so the third Number must have(2²*3²) as it`s factor.
Since L.C.M is the Product of Highest power of Common Prime Factor, So the Third
number must have 3⁵ and 7² as it’s factor.
Therefore, Third number =2²*3⁵*7²

Hope it helps.

Thanks and regards,

Kushagra