Mathematics HCF and LCM Quiz

What is the relationship between the HCF, LCM, and the two numbers?

Given that one number is 45 and the HCF is 3, which calculation can be used to find the other number?

Using the provided values, what is the other number when one number is 45?

If the LCM of two numbers is 1170, which of the following numbers also has 3 as a factor?

What does it imply if two numbers share the same HCF of 3?

Relationship between HCF, LCM, and Numbers

The product of two numbers is equal to the product of their HCF and LCM.
The HCF is the highest common factor of two numbers, representing the largest number that divides both of them evenly.
The LCM is the least common multiple of two numbers, representing the smallest number that is a multiple of both.

Finding the Other Number

Calculation: To find the other number, use the formula:
- (Number 1 * Number 2) = HCF * LCM
- Rearranged to solve for Number 2: Number 2 = (HCF * LCM) / Number 1
Applying to the example:
- Number 1 = 45
- HCF = 3
- LCM = (45 * Number 2) / 3
- To find Number 2, we need the LCM.

Determining Factors of the LCM

If the LCM of two numbers is 1170, it indicates that 1170 is divisible by both numbers.
Any number that is a factor of the LCM (1170) shares a common factor with both numbers.
Since the HCF is 3, both numbers have 3 as a factor.

If two numbers share the same HCF of 3, it means that both numbers are divisible by 3.
It does not necessarily imply they have other common factors, but it guarantees that they have 3 in common.

Test your understanding of the relationship between the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) with numbers. This quiz includes calculations involving given numbers and their factors, specifically focused on the values of 45 and 3. Analyze different scenarios and determine implications when two numbers share an HCF.