Answer :
Final answer:
To find the larger number when given the H.C.F, L.C.M, and the ratio, calculate the product of H.C.F and L.C.M and use the ratio to express the numbers. By solving the resulting equations, you can deduce the value of the larger number.
Explanation:
To find the larger of the two numbers when given the H.C.F and L.C.M, along with the ratio of the numbers, we use the relationship between the H.C.F, L.C.M, and the product of the two numbers. The formula is H.C.F × L.C.M = Product of the two numbers. Given the H.C.F (Highest Common Factor) is 84 and the L.C.M (Least Common Multiple) is 21, we can calculate the product of the two numbers as 84 × 21.
Let's denote the two numbers as A and B, with A being the smaller number and B the larger. With the given ratio A:B = 1:4, we can express B as 4 × A. Now the product of the numbers A × B equals A × (4 × A), which simplifies to 4A².
So, we get the equation 84 × 21 = 4A². Solving for A, we get the value of the smaller number. To find B, we multiply this value by 4, resulting in the value of the larger number. Mathematically, we'll solve this as follows:
- Carrying out the calculations, the larger number B is found to be 168, which answers the student's question.
