Maths with Gears | English

I have two gears given to me by a friend. We will play a game with them. Here are two gears – one big, the other small in mesh with each other. The big gear has 32 teeth and the smaller one has 16 teeth. The arrows of both gears point towards each-other. The question is – after how many turns of the smaller gear will the arrows of the two gears meet again. For the solution rotate the small gear in the clockwise direction. This is after one rotation. You will see that both the arrows meet after 2 rotations. This was quite easy. So, let us make it more challenging.
Now I will replace the 16-teeth gear with a larger one having 24-teeth. Once again I will rotate the small gear. After how many rotations of the smaller gear will the arrows of the two gears touch again. This is one rotation. Then two and three. Finally, when the small gear completes 4 rotations do the arrows of the 24 and 32 teeth gears meet again? What is the LCM of these two numbers? It is smallest multiple common to both the numbers. The multiples of 24 are 48, 72, 96, 120 and so on. The multiples of 32 are 64, 96, 128, 160 and so on. We can also visualize them in a Venn diagram. So the LCM of 24 and 32 is 96 – and it will take the small gear 4 turns and the big gear 3 turns so that their arrows meet again.

This work is supported by IUCAA (www.iucaa.in) and TATA Trust (http://www.tatatrusts.org/) and (www.tata.com/aboutus/sub_index/Tata-trusts)

TATA Trust: Education is one of the key focus areas for Tata Trusts, aiming towards enabling access of quality education to the underprivileged population in India. To facilitate quality in teaching and learning of Science education through workshops, capacity building and resource creation, Tata Trusts have been supporting Muktangan Vigyan Shodhika (MVS), IUCAA's Children’s Science Centre, since inception. To know more about other initiatives of Tata Trusts, please visit www.tatatrusts.org

Credits:,Ashok Rupner, Manish Jain, Pradnya Pujari, Shivaji Mane, Jyoti Hiremath, Arvind Gupta

Dubbed in Punjabi by Bipanmeesh Kaur, Delhi Public School, Ludhiana

Видео Maths with Gears | English канала Arvind Gupta