LCM and HCF Questions with Solutions | Set 1 (Q1 to Q10)

This set contains LCM and HCF Questions with Solutions — Set 1 (Q1 to Q10) covering a mix of question types and difficulty levels — from basic to advanced — exactly as asked in real competitive exams.

Solutions are written in a simple, step-by-step notebook style for easy self-study and quick understanding. Each solution is broken down step by step so even the toughest question feels easy. These questions are hand-picked for students preparing for SSC CGL, SSC CHSL, CAT, Bank PO, Bank Clerk, UPSC CSAT, Railway RRB, AMCAT, eLitmus, TCS NQT and all campus placement aptitude tests. International students preparing for GRE, GMAT, SAT, ACT, MAT and all Numerical Reasoning Tests will find these equally useful.

✏️ Attempt each question on your own first — then check the solution below.

1. Find the greatest weight which can be contained exactly in 80 kg & 100 kg.

2. Find the LCM of 120, 162 and 198.

3. Find LCM of 2.4, 0.36 and 7.2.

4. Find LCM of \(\frac{8}{{15}},\frac{3}{{10}},\frac{9}{{40}}\).

5. Find HCF of \(\frac{8}{{15}},\frac{3}{{10}},\frac{9}{{40}}\).

6. The LCM of two numbers is 1280, their HCF is 25 and one of the number is 80. Find the other number.

7. The HCF of two numbers is 42 and their LCM is 2646. Find the numbers if sum of the numbers is 672.

8. The LCM of two numbers is 15 times their HCF. The sum of their LCM & HCF is 800. If one of the number is 150 then find the other number.

9. Two numbers have 18 as their HCF and 153 as their LCM. Then how many pairs of such numbers are possible ?

10. Find the LCM of 48, 168, 324 and 1400.

1. Find the greatest weight which can be contained exactly in 80 kg & 100 kg.
Sol:
required weight = HCF(80, 100)

= 20 kg         Answer

2. Find the LCM of 120, 162 and 198.
Sol:

∴ LCM = 2 × 2 × 2 × 3 × 3 × 3 × 3 ×5 × 11
= 35460     Answer

3. Find LCM of 2.4, 0.36 and 7.2.
Sol:
To calculate the LCM of decimal integers, make the decimal integers into whole numbers multiplying with any friendly numbers i.e. 10, 100, 1000, ……….. etc.
Now find out LCM of these whole numbers.
Finally divide this LCM by that friendly number which we used earlier.

∴ LCM = 2⁴ × 3² × 5 = 720
∴ required LCM = \(\frac{{720}}{{100}}\) = 7.2           Answer

4. Find LCM of \(\frac{8}{{15}},\frac{3}{{10}},\frac{9}{{40}}\).
Sol:
= \(\frac{{LCM\;of(8,3,9)}}{{HCF\;of(15,10,40)}}\) 
= \(\frac{{72}}{5}\)    Answer

5. Find HCF of \(\frac{8}{{15}},\frac{3}{{10}},\frac{9}{{40}}\).
Sol:
= \(\frac{{HCFof(8,3,9)}}{{LCMof(15,10,40)}}\)
= \(\frac{1}{{120}}\)    Answer

6. The LCM of two numbers is 1280, their HCF is 25 and one of the number is 80. Find the other number.
Sol:
Product of numbers = LCM × HCF
x × 80 = 1280 × 25
x = 400    Answer

7. The HCF of two numbers is 42 and their LCM is 2646. Find the numbers if sum of the numbers is 672.
Sol:
Let numbers are 42x & 42y where x & y are co-prime.
∴ 42xy = 2646
xy = 63 ⟶ 3 × 3× 7
possible pairs of (x, y) are:
(1, 63)❌ ⟶ Numbers sum not 672
(3, 21)❌ ⟶ Not co-prime
(9, 7)✅ ⟶ Numbers sum = 42(9 + 7)
                                          = 672
∴ Numbers are:
42x = 42 × 9 = 378
42 y = 42 × 7 = 294        Answer

8. The LCM of two numbers is 15 times their HCF. The sum of their LCM & HCF is 800. If one of the number is 150 then find the other number.
Sol:
LCM = 15HCF
LCM + HCF = 800
15HCF + HCF = 800
HCF = 50
∴ LCM = 15 × 50 = 750
∴ 50 × 750 = 150 × x
x = 250     Answer

9. Two numbers have 18 as their HCF and 153 as their LCM. Then how many pairs of such numbers are possible ?
Sol:
Numbers are 18x & 18y where x & y are co-prime
∴ 18xy = 153
xy = 8.5 ⟵ Not a whole Number
So No such pair is possible     Answer

10. Find the LCM of 48, 168, 324 and 1400.
Sol:
Method(1):

∴ LCM = 2⁴ × 3⁴ × 5² × 7 = 226800     Answer

Method(2):

Method(3):

∴ LCM = 2⁴ × 3⁴ × 5² × 7 = 226800           Answer

✅ Well done on completing Set 1!

Continue practising with LCM and HCF Questions 11 to 20 → Set 2 or revisit the LCM and HCF Concept Page to strengthen your formulas and tricks before moving ahead.

Consistent practice is the key to mastering LCM and HCF for SSC CGL, SSC CHSL, CAT, Bank PO, Bank Clerk, UPSC CSAT, Railway RRB, AMCAT, eLitmus, TCS NQT and international exams including GRE, GMAT, SAT, ACT, MAT and all Numerical Reasoning Tests. Want to understand the concept better? Read about LCM on Wikipedia before attempting the next set.

This page is part of our complete series of LCM and HCF questions with solutions for competitive exams — covering every question type from basic to advanced so you can build speed, accuracy and confidence. Practising these questions regularly will also strengthen your core LCM and HCF concept before your exam day.