Question

The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, find the other number.​

Answer 1

$hcf \times lcm = product \: of \: two \: numbers$

$hcf = x$

$lcm = 14x$

$x + 14x = 600$

$15x = 600$

$x = 40$

$lcm = 40$

$hcf = 560$

$one \: number \: is \: 280$

$another \: number\: is \: y$

$hcf \times lcm = product \: of \: two \: numbers$

$40 \times 560 = 280 \times y$

$y = \frac{40 \times 560}{280}$

$y = 80$

Answer 2

➤ Answer

• Second number = 80.

➤ Given

• The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. One of the number is 280.

➤ To Find

• The other number.

➤ Step By Step Explanation

Given that the LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. One of the number is 280.

We need to find the second number.

So let's do it !!

➠ Assumption

Let LCM be 14x and HCF be x.

➠ Equation

14x + x = 600

➠ Solution of equation

14x + x = 600

15x = 600

x = 600/15

x = 40

Hence, LCM = 14x => 560 and HCF = x => 40

Now, we know that ⤵

➠ Formula

HCF × LCM = 1st number × 2nd number

➠ By substituting the values

$\longmapsto\tt560\times40 = 280\times 2nd\:number$

$\longmapsto\tt22400 = 280\times 2nd\:number$

$\longmapsto\tt\cancel\cfrac{22400}{280} = 2nd\:number$

$\longmapsto\tt\green{80 = 2nd\:number}$

Therefore second number = 80.

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