Question

Two numbers are in the ratio 3 : 4 and their LCM is 120. The sum of the numbers is _________.

Answer 1

Let the two numbers be 3x and 4x.

HCF of (3x, 4x) = x

We know that,
Product of two numbers = LCM × HCF

$$\begin{gathered} \Rightarrow 3x\times 4x=120\times x \\ \Rightarrow 12x^2=120x \\ \Rightarrow 12x=120 \\ \Rightarrow x=\frac{120}{12} \\ \Rightarrow x=10 \\ \mathrm{Therefore},\mathrm{first}\mathrm{number}\mathrm{is}3\times 10=30\mathrm{and}\mathrm{second}\mathrm{number}\mathrm{is}4\times 10=40. \end{gathered}$$

Sum of the numbers = 30 + 40 = 70.

Hence, the sum of the numbers is 70.