Question

Plz tell the tricks to solve lcm nd hcf word problems. ​

Answer 1

Answer:

Published on Sunday, July 21, 2013

LCM i.e. least common multiple is a number which is multiple of two or more than two numbers. For example: The common multiples of 3 and 4 are 12,24 and so on. Therefore, l.c.m.is smallest positive number that is multiple of both. Here, l.c.m. is 12.. HCF i.e. highest common factor are those integral values of number that can divide that number. LCM and HCF problems are very important part of all competitive exams.  

Step-by-step explanation:

1) Product of two numbers = Their h.c.f. * Their l.c.m.

2) h.c.f. of given numbers always divides their l.c.m.

3) h.c.f. of given fractions =     h.c.f. of numerator      

                                               l.c.m. of denominator

4) l.c.m. of given fractions =    l.c.m. of numerator      

                                              h.c.f. of denominator

5) If d is the h.c.f. of two positive integer a and b, then there exist unique integer m and n, such that

    d = am + bn

6) If p is prime and a,b are any integer then P ,This implies   P or P

                                                                    ab                       a      b

7) h.c.f. of a given number always divides its l.c.m.

Most important points about l.c.m. and h.c.f. problems :

1) Largest number which divides x,y,z to leave same remainder = h.c.f. of y-x, z-y, z-x.

2) Largest number which divides x,y,z to leave remainder R (i.e. same) = h.c.f of x-R, y-R, z-R.

3) Largest number which divides x,y,z to leave same remainder a,b,c  = h.c.f. of x-a, y-b, z-c.

4) Least number which when divided by x,y,z and leaves a remainder R in each case = ( l.c.m. of x,y,z) + R