Math Problem Statement

answeer

Product of two numbers is 9152 and their HCF is 8. What is the LCM of the numbers?

Solution

To solve the problem, we use the relationship between the product of two numbers, their HCF, and their LCM:

Product of two numbers=HCF×LCM\text{Product of two numbers} = \text{HCF} \times \text{LCM}

Given:

  • Product of two numbers = 9152
  • HCF = 8

We calculate the LCM:

LCM=Product of two numbersHCF=91528=1144\text{LCM} = \frac{\text{Product of two numbers}}{\text{HCF}} = \frac{9152}{8} = 1144

Answer:

The LCM of the two numbers is 1144.

Would you like me to explain further? Here are related questions for practice:

  1. What is the relationship between HCF, LCM, and the product of two numbers?
  2. Can the LCM of two numbers ever be smaller than their HCF? Why or why not?
  3. If the HCF of two numbers is 1, how does that affect their LCM?
  4. How can the LCM of two numbers be determined if their product and HCF are known?
  5. How does changing the HCF affect the LCM when the product remains constant?

Tip: Always simplify calculations by using the relationship Product=HCF×LCM\text{Product} = \text{HCF} \times \text{LCM} for efficiency.

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Math Problem Analysis

Mathematical Concepts

Number Theory
LCM (Least Common Multiple)
HCF (Highest Common Factor)

Formulas

Product of two numbers = HCF × LCM

Theorems

Relationship between HCF, LCM, and Product of Numbers

Suitable Grade Level

Grades 6-8