Two numbers have an HCF of 7 and an LCM of 84. If one of the numbers is 21, what

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Question: Two numbers have an HCF of 7 and an LCM of 84. If one of the numbers is 21, what is the other number? (2023)

Options:

Correct Answer: 42

Exam Year: 2023

Solution:

Using the relationship between HCF, LCM, and the numbers: (21 * x) / 7 = 84. Solving gives x = 42.

Two numbers have an HCF of 7 and an LCM of 84. If one of the numbers is 21, what is the other number? (2023)

Two numbers have an HCF of 7 and an LCM of 84. If one of the numbers is 21, what is the other number? (2023)

Step 1: Understand the problem. We have two numbers, one is 21, and we need to find the other number. The HCF (Highest Common Factor) is 7, and the LCM (Lowest Common Multiple) is 84.
Step 2: Recall the relationship between HCF, LCM, and the two numbers. The formula is: (Number 1 * Number 2) / HCF = LCM.
Step 3: Substitute the known values into the formula. Here, Number 1 is 21, HCF is 7, and LCM is 84. So, we write: (21 * x) / 7 = 84, where x is the other number we want to find.
Step 4: Simplify the equation. Multiply both sides by 7 to eliminate the denominator: 21 * x = 84 * 7.
Step 5: Calculate 84 * 7. This gives us 588, so now we have: 21 * x = 588.
Step 6: Solve for x by dividing both sides by 21: x = 588 / 21.
Step 7: Calculate 588 / 21. This gives us x = 28.
Step 8: Therefore, the other number is 28.

HCF and LCM Relationship – The relationship between the highest common factor (HCF) and the least common multiple (LCM) of two numbers is given by the formula: (Number1 * Number2) / HCF = LCM.
Finding Unknowns – Using known values to find an unknown number in a mathematical relationship.