Question 129
The HCF and LCM of two numbers are 8 and 48 respectively. If the ratio of the two numbers is 2 : 3, then the larger of the two numbers is:
Solution
Given that, H C F = 8 and LC M = 48
let numbers are 2a and 3a Where " a" is a common factor
so we use HCF and LCM formula,
$$HCF\times LCM = 2a\times3a $$
$$\Rightarrow 8\times 48 = 6a^2 $$
$$\Rightarrow a^2 = \dfrac{8 \times48}{6} $$
$$\Rightarrow a^2= 64 $$
$$\Rightarrow a = 8 $$
then the largest number = 3a = $$3\times8$$=24Ans
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