# QUESTIONS ON LCM & HCF (PART-III)

#### QUERY 21

**There are five hobby clubs in a college. The gardening group meets every second day, the electronic group meets every third day, the chess group meets every fourth day, the cricket club meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days?**

A) 3

B) 5

C) 10

D) 18

**MAHA GUPTA**

Obviously all the groups meet first in days equal to the number of LCM of the numbers they separately meet.

Hence, LCM of 2, 3, 4, 5, 6 = 60

Therefore the number of times they’ll meet together in 180 days = 180/60 = 3 (option ‘A’)

#### QUERY 22

**A milkman has 75 litres milk in one can and 45 litres in another. The maximum capacity of the container which can measure milk of either container exact number of times is?**

A) 1 litre

B) 5 litres

C) 15 litres

D) 25 litres

**MAHA GUPTA**

To measure exact number of times, the number must be a factor of the given capacities of milk. But we have to find the find the maximum of capacity of the container, so we need to find the HCF of 75 and 45.

Now HCF of 75 and 45 = 15 (option ‘C’)

#### QUERY 23

**The LCM of two multiples of 12 is 1056. If one of the numbers is 132, the other number is?**

A) 12

B) 72

C) 96

D) 132

**MAHA GUPTA**

The two numbers are multiples of 12, means 12 is their HCF

We know if one of the numbers is given, the other number = ^{LCM*HCF}⁄_{One of numbers}

So, The other number = ^{1056*12}⁄_{132}

= 96 (option ‘C’)

#### QUERY 24

**A number N is divisible by 6 but not divisible by 4. Which of the following will not be an integer?**

A) ^{N}⁄_{3}

B) ^{N}⁄_{2}

C) ^{N}⁄_{6}

D) ^{N}⁄_{12}

**MAHA GUPTA**

As the number is divisible by 6 and not divisible by 4, means the number is not divisible by the LCM of 6 and 4 also as in that case if we divide the number by the LCM of both, we’ll get our answer in decimal (not an integer).

Now LCM of 6 and 4 = 12

Therefore, the number ^{N}⁄_{12 }is not an integer.