Question

The LCM of two numbers is 56 times of their HCF. If one of the numbers is 315 and sum of their LCM and HCF is 2565, then the other number is: ​

Answer 1

Step-by-step explanation:

LCM=56x

x+56x=456

there for x=8

so,lcm is 448

and hcf is 8.

LCM * HCF=56 * x

8* 448 56 * x

x=8 * 448/56

answer is 64.

Step-by-step explanation:

Answer 2

Answer:

The second number is 360

Step-by-step explanation:

Given,

LCM of  two numbers is 56 times their HCF

The sum of their LCM and HCF is 2565

One number is 315

To find,

The other number

Solution:

Recall the concept:

LCM×HCF = Product of numbers ----------------(A)

Let 'x' the LCM and 'y' be the HCF of the two numbers

Since the LCM of  two numbers is 56 times their HCF, we have

x = 56y --------------(1)

Since The sum of  LCM and HCF of two numbers is 2565, we have

x+y = 2565 -----------(2)

Substituting the value of 'x' from equation (1) in equation (2) we get

56y + y = 2565

57y = 2565

y = 45

HCF of the numbers = 45

LCM of the numbers = 56y = 56×45 = 2520

Product of LCM and HCF = 2520×45 = 113400

Let 'z' the second number,

Since one number is 315, substituting the values in equation(A) we get

113400 = 315z

z = $\frac{113400}{315}$ = 360

Hence the second number is 360

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