Question 68

The HCF and the LCM of two numbers are 35 and 840, respectively. If the ratio of the two numbers is 3 : 8, then the smaller of the two numbers is:

Solution

As we know that the product of HCF and LCM of two numbers is equal to the product of these two numbers.

If the ratio of the two numbers is 3 : 8.

Let's assume the two numbers are 3y and 8y.

The HCF and the LCM of two numbers are 35 and 840, respectively.

$$HCF\times\ LCM\ =\ product\ of\ two\ numbers$$

$$35\times840\ =\ 3y\times\ 8y$$

$$35\times35\ =\ y\times y$$

So y = 35

Smaller of the two numbers = 3y

= $$3\times35$$

= 105

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