Lesson Light flashes on a Christmas tree and a Least Common Multiple

Light flashes on a Christmas tree and a Least Common Multiple

Problem 1

Find the least common multiple of 3, 4, 10.


Prime factor

3: 3

4: 2*2

10: 2*5


LCM = 3*2*2*5 = 60 seconds. All light flash on at 10:01.


At that time, 1st set flashes 20 times, the 2nd set flashes 15 times, the 3rd set flashes 6 times.  

Problem 2

You should find the Least Common Multiple of the numbers 60 and 48.


    60 = 12*5;  48 = 12*4;  therefore, LCM(60,48) = 12*4*5 = 240.


ANSWER.  The two bells ring simultaneously every 240 minutes, i.e. every 4 hours.

Problem 3

It is about finding the Least Common Multiple LCM  of the numbers  14 and 6.


To find LCM, you use prime decomposition of the two numbers, 14 and 6


    14 = 2*7;   6 = 2*3.


Then you take all participating prime numbers, 2, 3 and 7,  and raise each prime to the maximum participating degree.


Doing this way, you get factors  2, 3 and 7.


To get LCM, you multiply these factors:  2*3*7 = 42.


    LCM(14,6) = 7*2*3 = 42.


ANSWER.  In 42 days.

Problem 4

This problem is to find the Greatest Common Divisor (GCD) of the numbers 286, 390 and 468.


These numbers have common prime divisors 13 and 2 and have no other common prime divisors.


So, their greatest common divisor is 13*2 = 26.


THEREFORE, the three friends should put 26 sweets into each box.


Doing this way, they will fill   = 44 boxes.    ANSWER