WORKSHEET ON HCF AND LCM

How to Find the HCF of Two Numbers and Three Numbers

1)  18, 48   Solution

2)  30, 42   Solution

3)  18, 60    Solution

4)  27, 63    Solution

5)  36, 84    Solution

6)  34, 102    Solution

Problem 7 :

The length of a big hall is 2000 cm and its breadth is 1600 cm. What would be the length of the longest tape that can be used to measure the length and breadth of the hall in an exact number of times?

Solution

Problem 8 :

A hall 33 m long and 16 m wide is to be paved with square floor tiles. What would be the length of the largest tile that can be used such that the entire floor is covered?

Solution

Problem 9 :

What is the maximum number of equal squares of the biggest possible size that can be cut out of a piece of cardboard 48 cm broad and 64 cm long? what would be the length of each square?

Solution

Problem 10 :

Two bags of wheat contain 42 kg and 56 kg of wheat, respectively. What is the greatest weight that can be used to measure the wheat in each bag an exact number of times ? How many times will it take to weigh all the wheat in the two bags using this weight ?

Solution

Problem 11 :

The ratio of two numbers is 3 : 4 and their HCF is 4. Their LCM is

a)  12    b)  16      c)  24     d) 48

Solution

Problem 12 :

The sum of two numbers is 216 and their HCF is 27. The numbers are :

a)  27, 189    b)  81, 189     c)  108, 108     d) 154, 162

Solution

Problem 13 :

The sum of two numbers is 528 and their HCF is 33. The number is pairs of numbers satisfying the above conditions is :

a)  4      b)  6       c)  8      d)  12

Solution

Find the least common multiple using ladder method.

Problem 1 :

70, 105, 175

Solution

Problem 2 :

91, 112, 49

Solution

Problem 3 :

18, 54, 81

Solution

Problem 4 :

12, 45, 75

Solution

Problem 5 :

The sum of two numbers is 528 and their HCF is 33. The number of pairs of numbers satisfying the above conditions is 

a)  4      b)  6     c)  8     d)  12

Solution

Problem 6 :

The number of number pairs lying between 40 and 100 with thier HCF as 15 is 

a)  3      b)  4     c)  5     d)  6

Solution

Problem 7 :

The HCF of two numbers is 12 and their difference is 12. The numbers are 

a)  66, 78      b)  70, 82     c)  94, 106    d)  84, 96

Solution

Problem 8 :

The product of two numbers is 4107. IF the HCF of these numbers is 37, then the greater number is 

a)  101      b)  107     c)  111     d)  185

Solution

Problem 9 :

The product of two numbers is 1320 if their HCF is 6. The LCM of the numbers is 

a)  220      b)  1314     c)  1326     d) 7920

Solution

Problem 10 :

The HCF and LCM of two numbers are 50 and 250 respectively. If the first number is divided by 2, the quotient is 50. The second number is :

a)  50      b)  100     c)  125     d) 250

Solution

Problem 11 :

The greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case is :

a)  64      b)  124     c)  156     d) 260

Solution

Finding HCF and LCM using Ladder Method and Prime Factorization Method

Reference for Ladder Method -----> Solution

Reference for Prime Factorization Method -----> Solution

Word Problems on LCM 

1)  There bells toll together at 10 am. The first bell tolls every 10 seconds, the second tolls every 15 seconds, and the third tolls every 20 seconds. At what time will the three bells toll together next?

2)  There are three tigers in a jungle. All three roar together at 6.00 am as soon as they wake up. Thereafter one roars every 20 seconds, another roars every 25 seconds and third roars every 30 seconds. When will the three tigers roar together again? When will they roar together after that?

3)  Water starts to drip out of two taps. A drop of water comes out of one tap every 5 seconds and out of the other tap every 7 seconds. After two drop fall together from the two taps. When will be the next time that two drops will again fall from the two taps at the same time?

4)  There are three marigold plants in flower pots. A flower bloom on one plant every 2 days. The second plant bears a flower every 3 days and the third one every 4 days. If there is a flower on each of the three plants today. When will the flowers bloom together again ?

5)  In a morning walk, three persons step off together. Their steps measure 80 cm, 85 cm, and 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

Solution

Answers :

1)  After 60 seconds three bells will ring together.

2)  After 5 minutes, the three tigers will roar together.

3)  After 35 second water will drip out

4)  After 12 days, the flowers on the three plants will bloom together.

5)  Minimum distance is 12240 cm.