Question

the lcm of two numbers is two times thier hcf if one of the numbers are 125, and the sum of the lcm and hcf is 1150 what is the other number

Answer 1

Correct Question:

The LCM of two numbers is 45 times their HCF if one of the numbers is 125 and sum of their HCF and LCM is 1150. What is the other number?

Answer:

• The other number is 225.

Step-by-step explanation:

Given that:

• The LCM of two numbers is two times thier HCF.
• i.e., LCM = 2HCF

• One of the numbers are 125.

• The sum of the LCM and HCF is 1150.
• i.e., LCM + HCF = 1150

To Find:

• What is the other number.

We have:

⇒ LCM = 45HCF _____(i)

⇒ LCM + HCF = 1150

⇒ 45HCF + HCF = 1150 [from eqⁿ(i)]

⇒ 46HCF = 1150

⇒ HCF = 1150/46

⇒ HCF = 25

In equation (i),

⇒ LCM = 45HCF

⇒ LCM = 45 × 25

⇒ LCM = 1125

Let us assume:

• The other number be x.

We know that:

• LCM × HCF = Product of the numbers

Now we have:

• LCM = 1125
• HCF = 25
• One of the numbers = 125
• Other number = x

Finding the other number:

According to the question.

⟶ 1125 × 25 = 125 × x

⟶ 28125 = 125x

⟶ x = 28125/125

⟶ x = 225

∴ Other number = 225

Answer 2

Given :

• The LCM of two numbers is 45 times thier HCF if one of the numbers are 125, and the sum of the LCM and HCF is 1150.

To find :

• Other number

Solution :

• As In the question it is given LCM of two is 45 times. So, Let us assume the LCM be y and HCF be 45y and their sum is 1150. First Number is already given to us that is 125, then we can easily find the other required number by using LCM × HCF = Product of two given numbers

Let us assume the number y

→ y + 45y = 1150

→ 46y = 1150

→ y = 1150/46

→ y = 25

• LCM = 25

• HCF = 25 × 45 = 1125

Now, Finding other number

LCM × HCF = Product of two numbers

→ 25 × 1125 = 125 × y

→ 28125 = 125y

→ y = 28125/125

→ y = 225

Verification :

LCM × HCF = Product of two numbers

→ 25 × 1125 = 125 × 225

→ 28125 = 28125

Hence, Proved

∴ The other number is 225.