HCF & LCM | Playing with Numbers | Assessment | English | Grade 6

LCM stands for ___.

• Least Common Multiple

• Lowest Common Multiple

• Latest Common Multiple

• Option 1 and 2 both

Answer explanation

LCM stands for Lowest Common Multiple or Least Common Multiple.

What is LCM of 9,12,15?

• 1620

• 3

• 180

• 300

Answer explanation

Option 3 is correct as prime factors of 9, 12 and 15 are 2, 2, 3, 3, 5 hence LCM of 9, 12, 15 is 360

What is HCF of 345 and 265 ?

• 3

• 5

• 7

• 9

Answer explanation

Since, 345 = 3 x 5 x 23 And, 265 = 5 x 53 Hence, the common prime factor of both numbers is 5 Hence 5 is the HCF of given numbers.

Find the numbers whose LCM is 720 and HCF is 1 ?

• 45,40,38

• 40,48,45

• 36,32,47

• 24,37,41

Answer explanation

Option 2 is correct as 40,48,45 has lcm 720 and hcf 1 Option 1 is wrong as 45,40,38 has lcm 6840 and hcf 1 Option 3 is wrong as 36,32,47 has lcm 13536 and hcf 1 Option 4 is wrong as 24,37,41 has lcm 36408 and hcf 1

What is LCM of 160, 170, 90?

• 24840

• 24680

• 24500

• 24480

Answer explanation

Option 4 is correct as prime factors of 90,160,170 are 2,2,2,2,2,3,3,5,17 hence lcm of 90,160,170 are 24480 Option 1 is wrong as prime factors of 90,160,170 are 2,2,2,2,2,3,3,5,17 hence lcm of 90,160,170 are 24480 not 24840 Option 2 is wrong as prime factors of 90,160,170 are 2,2,2,2,2,3,3,5,17 hence lcm of 90,160,170 are 24480 not 24680 Option 3 is wrong as prime factors of 90,160,170 are 2,2,2,2,2,3,3,5,17 hence lcm of 90,160,170 are 24480 not 24500

In a morning walk, three persons step off together. Their steps measure 80 cm, 75 cm and 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

• 1440 cm

• 3600 cm

• 400 cm

• 1200 cm

Answer explanation

Here, the minimum distance when the three persons should walk so as to cover the same distance in complete steps will be the smallest multiple of 80 cm, 75 cm and 90 cm i.e. LCM of 80, 75 and 90 The prime factorisation of these numbers can be done as shown in the figure. From which we get the LCM of 80, 75 and 90 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 = 3600 Hence answer is 3600 cm i.e. 36 m

Two tankers contain 650 litres and 780 litres of kerosene oil respectively. Find the maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times.

• 120 L

• 150 L

• 130 L

• 170 L

Answer explanation

Here, the maximum capacity of the container which can measure 780 litre and 650 litre must be the HCF of these numbers. The prime factorisation of these numbers is shown in the figure. Here, 780 = 2 x 2 x 3 x 5 x 13 And, 650 = 2 x 5 x 5 x 13 Common factors are 2, 5, 13 HCF of 780 and 650 is, (2 x 5 x 13) i.e. 130 Hence, the highest capacity of the container must be 130 litre so that it can measure 780 litre and 650 litre complete number of times.