Two numbers have a Highest Common Factor (H.C.F) of 84 and a Least Common Multiple (L.C.M) of 21. If their ratio is 1:4, what is the larger number?

Explanation

Let the two numbers be x and 4x. According to the relationship between H.C.F and L.C.M, x × 4x = H.C.F × L.C.M. Therefore, 4x² = 84 × 21. Simplifying, x² = (84 × 21) / 4, which gives x = 21. The larger number is 4x = 84.