6. Application problems based on LCM and HCF

1. Meena has three different kind of chocolates. Each type has \(24\), \(30\) and \(18\) chocolates. Meena wants to divide each chocolate into groups so that every group on every type has the same number of chocolates, and there are no chocolate leftover. What is the maximum number of chocolates she can put into each group?

 

Solution:

 

Number of chocolates in each type \(=\) \(24\), \(30\) and \(18\).

 

We have to find the maximum number of chocolates she can put into each group. This should give you an indication that here we have to calculate the HCF.

 

Factor of \(24\) \(=\) \(2 \times 2 \times 2 \times 3\)

 

Factor of \(30\) \(=\) \(2 \times 3 \times 5\)

 

Factor of \(18\) \(=\) \(2 \times 3 \times 3\)

 

HCF of \(24\), \(30\) and \(18\) \(=\) \(2 \times 3 = 6\)

 

Therefore a maximum of \(6\) chocolates can put into each group.

 

 

2. A doctor advises a patient to take a tablet every \(4\) hours and a syrup every \(6\) hours. If he take the medicine and syrup now, when will the patient take both at the same time?

 

Solution:

 

Medicine should take for every \(4\) hours.

 

Syrup should take for every \(6\) hours.

 

We need to find when will the patient take both medicine and syrup at the same time. This gives you an indication that here we have to calculate the LCM.

 

Multiples of \(4\) \(=\) \(4\), \(8\), \(12\), \(16\), …

 

Multiples of \(6\) \(=\) \(6\), \(12\), \(18\), ..

 

LCM of \(4\) and \(6\) \(=\) \(12\)

 

Therefore, the patient will take both medicines at the same time after \(12\) hours.