Mathematics — Standard (041) — CBSE Class 10 board question

Let the two numbers be $4x$ and $5x$, where $x$ is the HCF.

Given HCF = 11, so $x = 11$.

∴ The two numbers are $4 \times 11 = 44$ and $5 \times 11 = 55$.

Using the relation: HCF × LCM = Product of the two numbers

$$11 \times \text{LCM} = 44 \times 55$$

$$\text{LCM} = \frac{44 \times 55}{11} = \frac{2420}{11} = \boxed{220}$$

Source: Chapter 1, Section 1.2

• Since two numbers are in ratio 4:5, write them as 4k and 5k. The HCF of 4k and 5k is k (since 4 and 5 are coprime), so k = HCF = 11.
• Apply the standard result: HCF × LCM = product of two numbers. Examiners expect you to state this formula explicitly before using it.
• Writing the numbers first (44 and 55) and then applying the formula earns full method marks even if arithmetic slips slightly.