2.  If x<y<z  When all are co-prime no. then HCF is 1  Maximum HCF could be x only  Minimum LCM is z when z is a multiple of x,y,z  Maximum LCM is x*y*z when all are co-prime no.

3. Find the HCF and LCM of 102,54, 72 102= 2×3×17 54= 2×3³ 72=2³×3² HCF= 2×3 [Least power of all the prime no.] LCM= 2³×3³×17 = 3672 [Max. power of all the prime no.]

4.  LCM is a multiple of HCF  For 2 no. HCF*LCM= product of two no.  When fractions are in simplest form the:  HCF of fractions= HCF of numerator/LCM of Denominator  LCM of fractions= LCM of numerator/HCF of Denominator

5. Q.1) Find HCF and LCM N= 20²×11, 33×100, 150²×22 Q.2) Big log of woods measuring 15×18×24 cm needed to be cut into some cubes such that each cube should have max. volume and nothing is left over. Find the total no of cubes?

6. S.1) 20²×11= 2⁴×5²×11 33×100= 3×11×5²×2² 150²×22= 3²×5⁴×2³×11 HCF= 11×5²×2²=1100 LCM= 3²×5⁴×2 ⁴ ×11= 2520

7. S.2) Wood= 15, 18,24 = 3×5,3²×2,2³×3 HCF =3 which would be dimension of the cube Total no. of cubes= 5 × 6×8= 240

8.  Q.) Two cyclists were preparing for Olympics in the Yamuna velodrome. The first cyclists take 10 min to cover one full round, while second cyclists take 9 min. find when would they both be together at the starting block if they both started simultaneously.  Q.) A rectangular piece of cloth has dimensions 16m×6m. What is the least no. of equal squares that can be cut out off this cloth such that no. cloth is wasted?

9.  Q. In a school 437 boys and 342 girls have been divided in to classes, such that each class has the same no. of students and no class has boys and girls mixed. What is the least no. of classes needed?  Q. Manas and his girl friend met at Nehru place after a long time. Manas stays at vivek vihar and his girl friend stays in gurgoan. Both of them commute by bus. They reached the bus stop, and got to know that a bus had left just then for each of their destinations. Neither wanted to leave the other alone at the bus stop. If the frequency of the buses to gurgoan was 7 min and to vivek vihar was 11 min.. a) How long would they wait at the bus stop? b) How many buses going to their destination would each one decide not to board?