Question

The sum the HCF and LCM of two number is 680 and the LCM is 84 times
the HCF. If one of the number be 56, find the other.

Answer 1

✬ The other number is 96 ✬

Step-by-step explanation:

Given:-

• Sum of HCF and LCM is 680
• LCM is 84 × HCF
• One number of HCF and LCM is 56.

To find:-

• Other number of HCF and LCM.

Solution:-

Now,finding the HCF,

Using formula,

• LCM + HCF = sum of two numbers

Here,

• HCF = x
• LCM = 84x

$\\ :\implies\sf{x + 84x = 680} \\ \\ :\implies\sf{85x = 680} \\ \\ :\implies\sf{x = \frac{680}{85} }\\ \\ :\implies \underline{\boxed{\frak{x = 8}}} \: \blue{ \bigstar}$

Therefore,

• HCF = x = 8
• LCM = 84x = 84(8) = 672.

Then,Finding the other number of HCF and LCM.

Using formula,

• LCM × HCF = a × b

Where,

• LCM = 672
• HCF = 8
• a = 56
• other number = b

$\\ :\implies\sf{672 \times 8 = 56 \times b} \\ \\ :\implies\sf{5376 = 56b} \\ \\ :\implies\sf{b = \frac{ \cancel{5376}}{ \cancel{56}}} \\ \\ :\implies \underline{ \boxed{\frak{b = 96}}} \: \red{ \bigstar}$

Therefore,

• The other number is 96.

Answer 2

Answer:

Step-by-step explanation: Let a and b are the two numbers and also let hcf of two numbers be=x, then the lcm of the two numbers=84x. Therefore, hcf of the two numbers=x=8 and lcm of the two numbers=84x=84(8)=672.

Step-by-step explanation:

Step-by-step explanation:

Let a and b are the two numbers and also let hcf of two numbers be=x, then the lcm of the two numbers=84x.

From the given statement, we get

x+84x=680x+84x=680

85x=68085x=680 no

x=8x=8

Therefore, hcf of the two numbers=x=8 and lcm of the two numbers=84x=84(8)=672.

Now, lcm

hcf=Productof two numberslcm×hcf=Product of two numbers

672×8=56b

56

672×8=56

b=96

b=96b=96

56

672×8

=b

b=96b=96

Thus, the other number is 96.