If the HCF of three numbers is 5 and their LCM is 300, what can be said about th
Practice Questions
Q1
If the HCF of three numbers is 5 and their LCM is 300, what can be said about the numbers?
They are all multiples of 5
They are all prime
They are all even
They are all odd
Questions & Step-by-Step Solutions
If the HCF of three numbers is 5 and their LCM is 300, what can be said about the numbers?
Step 1: Understand what HCF (Highest Common Factor) means. It is the largest number that divides all the given numbers without leaving a remainder.
Step 2: Note that the HCF of the three numbers is 5. This means that all three numbers must be multiples of 5.
Step 3: Understand what LCM (Lowest Common Multiple) means. It is the smallest number that is a multiple of all the given numbers.
Step 4: The LCM of the three numbers is 300. This means that 300 is the smallest number that can be formed by multiplying the three numbers together in some way.
Step 5: Since the HCF is 5, we can express each number as 5 times another number. For example, let the three numbers be 5a, 5b, and 5c, where a, b, and c are integers.
Step 6: Substitute these into the LCM formula. The LCM of 5a, 5b, and 5c can be expressed as 5 * LCM(a, b, c).
Step 7: Set up the equation: 5 * LCM(a, b, c) = 300.
Step 8: Divide both sides by 5 to find LCM(a, b, c): LCM(a, b, c) = 300 / 5 = 60.
Step 9: Conclude that the numbers can be expressed as multiples of 5, and their corresponding factors (a, b, c) must have an LCM of 60.
Highest Common Factor (HCF) – The largest number that divides all given numbers without leaving a remainder.
Lowest Common Multiple (LCM) – The smallest number that is a multiple of all given numbers.
Relationship between HCF and LCM – The product of the HCF and LCM of a set of numbers is equal to the product of the numbers themselves.
