# CAT Practice : Number System: HCF, LCM

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The following topics are covered in the CAT quant section from Number system - HCF, LCM. Detailed explanatory answers, solution videos and slide decks are also provided.
1. ### Number Theory - HCF LCM

How many pairs of integers (x, y) exist such that the product of x, y and HCF (x, y) = 1080?

1. 8
2. 7
3. 9
4. 12
2. ### Number Theory - Remainders LCM

Find the smallest number that leaves a remainder of 4 on division by 5, 5 on division by 6, 6 on division by 7, 7 on division by 8 and 8 on division by 9?

1. 2519
2. 5039
3. 1079
4. 979
3. ### HCF LCM - Theory

There are three numbers a,b, c such that HCF (a, b) = l, HCF (b, c) = m and HCF (c, a) = n. HCF (l, m) = HCF (l, n) = HCF (n, m) = 1. Find LCM of a, b, c. (The answer can be "This cannot be determined").

• HCF LCM, tough algebraic qn
• Hard
4. ### HCF basics

How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?

1. 12
2. 8
3. 15
4. 30
5. ### HCF LCM

How many pairs of positive integers x, y exist such that HCF (x, y) + LCM (x, y) = 91?

1. 10
2. 8
3. 6
4. 7
6. ### HCF basics

Sum of two numbers x, y = 1050. What is the maximum value of the HCF between x and y?

1. 350
2. 700
3. 1050
4. 525
7. ### HCF basics

The sum of two non co–prime numbers added to their HCF gives us 91. How many such pairs are possible?

1. 2
2. 4
3. 3
4. 6
8. ### HCF LCM basics

There are 2 numbers such that a > b, HCF (a, b) = h and LCM (a, b) = l. What is the LCM of a – b and b?

1. l
2. (a - b) b
3. (a - b) b / h
4. h (a - b)
(a - b) b / h
• HCF LCM basics
• Medium
9. ### No of sweet boxes

6 different sweet varieties of count 32, 216, 136, 88, 184, 120 were ordered for a particular occasion. They need to be packed in such a way that each box has the same variety of sweet and the number of sweets in each box is also the same. What is the minimum number of boxes required to pack?

1. 129
2. 64
3. 48
4. 97
10. ### Minimum number of students

In a large school auditorium, the students are made to sit to watch the programmes. If the teachers make a row of students of 16 each, there will be 12 students left. If they make rows of 24 each, then there will be 20 students left, if they make rows of 25 each, there will be 21 students left and if they make rows of 30 each, there will be 26 students left. What is the minimum number of students present in the school?

1. 1216
2. 1784
3. 1196
4. 2396
1196
• Minimum number of students
• Medium
11. ### Sum of the digits

LCM of 2 natural numbers p and q where p > q is 935. What is the maximum possible sum of the digits of q?

1. 1
2. 8
3. 5
4. 2
12. ### Number of Carpenters

4 logs of woods of lengths 5 1/4 m, 1 13/15 m, 3 1/2 m and 4 9/10 m are cut into small pieces, all of which have equal length. Each piece of wood is as lengthy as possible. Each cut piece is given to a set of 2 carpenters to work on something. How many carpenters are there in all to work?

1. 148
2. 210
3. 332
4. 266

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