Monday, 20 April 2009

Lowest Common Multiple

What is Lowest Common Multiple in
Arithmetic of Life?

In the primary school, our teacher taught us "Lowest Common Multiple" (LCM). He didn’t tell us why or what was its use in practice. The white man told us, and we followed, like sheep, monkey, or parrot. (We are still doing that.) I learnt in Marathi, which was then called vernacular, at my native village Katta in Sindhudurg District, in Konkan - one of the well-known biodiversity regions of the world.
Then, also, we kids knew for sure, that every paddy seedling that grows gives twenty-thirty grains; a tiny seed that grows into mighty banyan tree bears million fruits, shelters and feeds hundreds of birds, Vetal or genie makes it his home.
But in all this what is the "LCM"?

For 2+7/10/12/15/17 years, the students take education, at schools/ colleges, whatever they could afford. But they even do not know what the practical use of "LCM" is. They also don’t know, or don’t understand, how to feed themselves with the help of that education. They only know that they should get a job, an employment, for that they need luck and/or some influence, or be able to bribe the higher ones.
By then their first 25 years of age are gone! What a colossal waste of national youth energy!
That doesn’t happen with the children of peasants, traditional artisans. By the time boys and girls are fifteen years of age; they are graduated in their family arts: farming, pottery, smithy, carpentry, masonry, weaving etc. By then they come of age, attain puberty. They are ready to stand on their own feet – take responsibility. Then prepare for marriage at right age – eighteen years.
What is the "LCM" in all this?
My "Two-in-One" Question
It happened in 1985-86. I was attending "International Conference on School Buildings for Afro-Asian Countries" at Roorkee, Uttaranchal. The venue was "Central Building Research Institute" (CBRI). About five hundred (may be more) delegates from India and abroad were attending the meet.
Director of "National Council of Educational Research and Training" (NCERT) was to deliver the inaugural address. Since he couldn’t attend, NCERT’s Prof. Bhattacharya read his text. The usual time of Q&A followed.
Before anyone else, I grab the opportunity to ask my question.
‘I want to ask two questions. My first question: What is the "minimum" education for every citizen is a must?’
Entire auditorium laughed no sooner my question finished.
‘It seems you haven’t heard my question. I repeat. I asked,’ holding my note in hand, ‘what "minimum", not "maximum" education.’
Prof. Bhattacharya mumbled something, which he too must not have understood. Ignoring what happened I continued.
‘My second question: Why there are dropouts? Even from the primary schools a large number of students leave education midway.’
Four or five pundits tried impromptu some flimsy answers; they too knew it.
How could anyone answer, if never thought about it; never climbed down to earth to see what is happening in real life; if never knew what is "minimum"?
During the closing session, the organizers informed the delegates that my "two-in-one" question was repeated in each of eight workshops. However they did not reach any conclusive answer. This, of course, was expected. I also came to know that I was the only delegate who came by spending his own money, i.e., I did not represent any organization. The rest had come on the allowances paid by their respective governments or departments or institutions.
What is the "LCM" of this story?
In the following years I documented whatever I witnessed, encountered, experience at a ground level in the Education and beyond. Some has been published in journals and periodicals, some of it on my blogs. One of the earliest article "Indian Schooling" was published in India and the UK.

I intend to publish a sereis on "Lowest Common Multiple" in course of time. Your responses and reactions are valuable.
© Remigius de Souza, all rights reserved.


  1. i think now after reading your article, that with the series of such article, i'm going to end up with some questions,thoughts in my mind..more and more questions... and i will have to find the LCM of those all to reach any conclusion (if i wish that conclusion should exist)

    p.s. you set me thinking more :)

  2. Harshada,

    What you say is true. It is always a personal quest, where we enjoy utmost autonomy, where none can prevent us. If you see my previous posts on Education, you might see how I have been wandering – looking for directions...

    I am delighted.


  3. :)
    thanks remi..
    i'm too delighted to be in contact with the person like you..
    your canvas itself is very wide.. understanding it will only take lot of time for bachchha like me

  4. Harshada,
    All bachchas, being born after me, are ahead of me by that many years. Hence, I don’t call them kids – bachchas (as long as they remain bachchas, meaning, childlike, not childish. They are precious... and VIPs for me.

    Also, our bringing up (family etc), grooming (formal-informal schooling) and orientation matter most – irrespective of if a person is young or old.

    I am an author, but I don’t claim authority. Likewise whatever I hear or read, I make a point to check it at the ground reality – ground below my feet.

    Bes wishes,


  5. Harshada,
    I just made some alterations to this post. As I go through the comments, I wondered perhaps you may have forgotten this post in two years… I would love to learn about your discoveries!!!

  6. No I haven't forgotten the post.. And I wonder that you commented here to convey a message to me without knowing the minimal probability of me rechecking the post and I (I-dont-know-how) came to this page again !!!.. HAAAA...... I really wonder!
    Read my comments and thought I can write them in better English now!! :D

    Cheers (to such wonders!)


  7. I am delighted to hear from you... I use these facilities sometimes. I would love to learn about your second thoughts… after a period of time! :-D
    ~~ Remi