Find the best tutors and institutes for Class 10 Tuition
Q2(ii):
Find the LCM and HCF of the following pairs of integers and verify that LCM $\times$ HCF = product of the two numbers. (ii) 510 and 92
Solution :
Given: Two integers, $a = 510$ and $b = 92$.
To Find: The Highest Common Factor (HCF) and the Least Common Multiple (LCM) of the given integers, and to verify the relationship: $LCM \times HCF = \text{Product of the two numbers}$.
Step 1: Prime Factorization of the given numbers
We express each number as a product of its prime factors.
For $510$:
$510 = 2 \times 255$
$255 = 3 \times 85$
$85 = 5 \times 17$
$17 = 17 \times 1$
So, $510 = 2^1 \times 3^1 \times 5^1 \times 17^1$
For $92$:
$92 = 2 \times 46$
$46 = 2 \times 23$
$23 = 23 \times 1$
So, $92 = 2^2 \times 23^1$
Step 2: Determining HCF and LCM
HCF (Highest Common Factor): The HCF is the product of the smallest power of each common prime factor in the numbers.
Common prime factor is $2$. The smallest power of $2$ is $2^1$.
$HCF(510, 92) = 2^1 = 2$.
LCM (Least Common Multiple): The LCM is the product of the greatest power of each prime factor involved in the numbers.
Prime factors involved are $2, 3, 5, 17, 23$.
Greatest powers are $2^2, 3^1, 5^1, 17^1, 23^1$.
$LCM(510, 92) = 2^2 \times 3^1 \times 5^1 \times 17^1 \times 23^1$
$LCM(510, 92) = 4 \times 3 \times 5 \times 17 \times 23$
$LCM(510, 92) = 12 \times 5 \times 17 \times 23$
$LCM(510, 92) = 60 \times 17 \times 23$
$LCM(510, 92) = 1020 \times 23$
$LCM(510, 92) = 23460$.
Step 3: Verification of the relationship
We need to verify if $LCM \times HCF = a \times b$.
Left Hand Side (LHS):
$LCM \times HCF = 23460 \times 2$
$LCM \times HCF = 46920$.
Right Hand Side (RHS):
Product of numbers $= 510 \times 92$
$510 \times 92 = 510 \times (90 + 2)$
$= 45900 + 1020$
$= 46920$.
Since $LHS = RHS$, the relationship is verified.
Final Answer: The HCF is $2$, the LCM is $23460$, and the relationship $LCM \times HCF = \text{Product of the two numbers}$ is verified as $46920 = 46920$.
More Questions from Class 10 Mathematics Real numbers EXERCISE 1.1
- Q1(i): Express each number as a product of its prime factors: (i) 140
- Q1(ii): Express each number as a product of its prime factors: (ii) 156
- Q1(iii): Express each number as a product of its prime factors: (iii) 3825
- Q1(iv): Express each number as a product of its prime factors: (iv) 5005
- Q1(v): Express each number as a product of its prime factors: (v) 7429
- Q2(i): Find the LCM and HCF of the following pairs of integers and verify that LCM $\times$ HCF = product of the two numbers. (i) 26 and 91
- Q2(iii): Find the LCM and HCF of the following pairs of integers and verify that LCM $\times$ HCF = product of the two numbers. (iii) 336 and 54
- Q3(i): Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21
- Q3(ii): Find the LCM and HCF of the following integers by applying the prime factorisation method. (ii) 17, 23 and 29
- Q3(iii): Find the LCM and HCF of the following integers by applying the prime factorisation method. (iii) 8, 9 and 25
- Q4: Given that HCF (306, 657) = 9, find LCM (306, 657).
- Q5: Check whether $6^n$ can end with the digit 0 for any natural number $n$.
- Q6: Explain why $7 \times 11 \times 13 + 13$ and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$ are composite numbers.
- Q7: There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
CBSE Solutions for Class 10 Mathematics Real numbers
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Real numbers
Super Tutor
Badarpur, Delhi
11 yrs of
Exp
145 students
3602 hrs of classes completed
200
per hour
Online Classes
Tutor's home
I am utterly grateful to Akshay sir for his unending support and sincere guidance. He was such a big pillar of support in my board exams and his style of teaching is truly exceptional!!!! His notes, his previous year questions, his tips and his advices are really helpful for the board exams. I was able to score 97.2% in my boards because of his style of teaching. In fact all the topics he marked as important came in the board exams! Moreover he is a very hardworking and dedicated teacher with an unending passion to support and tutor children. I really am grateful to you Akshay sir Regards Nirvaan Rai Batch 2025-26
Super Tutor
Kodambakkam, Chennai
15 yrs of
Exp
57 students
3744 hrs of classes completed
800
per hour
Online Classes
With a decade of experience in teaching mathematics, physics, and chemistry for students from grades 8 through 12 across CBSE, IB, and ICSE boards, I offer a comprehensive educational approach that caters to a diverse range of curricula and learning needs. My academic background includes a BE and an MBA, equipping me with both technical and managerial skills that enhance my teaching methodology. Throughout my career, I have specialized in home tutoring, where I have developed a personalized approach to education that focuses on each student's unique needs and strengths. My sessions are designed to be interactive and engaging, fostering a learning environment where students feel supported and motivated. I conduct both online and offline classes, each lasting one hour, and utilize a variety of teaching tools to facilitate learning. I employ a whiteboard to visually explain concepts and provide question papers to help students practice and prepare for their exams. This hands-on approach ensures that students not only understand theoretical concepts but also develop problem-solving skills and confidence in their subjects. My commitment to delivering high-quality education and my extensive experience make me well-suited to guide students through their academic journey, helping them achieve their full potential in mathematics, physics, and chemistry.
Super Tutor
Nerul Sector 20, Thane
10 yrs of
Exp
62 students
2804 hrs of classes completed
1200
per hour
Online Classes
I have done b.Tech in electrical engineering from IIT KANPUR. I taught one year in akash institute patna, 2 years in fiitjee patna. Currently I am teaching in unacademy. I have taught more than 6000 jee and neet aspirants. In which more than 500 students are selected in iitand aiims. If some one is interested to improve their physics upto jee advanced level take help with me .And see the magic. I can help students in their all type of assignment from any institute like allen, fiitjee, narayna, akash, resonance. I can help students to solve both volume of h.C verma within two month if some one is intrested in solving I.E.Irodov join me and see the next level of physics. My way of teaching is so easy and so advanced that student will realyy enjoy it. Don't waste your time in making decision just join and experience my level
He is a very dedicated teacher with excellent knowledge on topic. He knows Subject very well and teach accordingly to kids.
Super Tutor
Basaveshwara Nagar, Bangalore
12 yrs of
Exp
12 students
3331 hrs of classes completed
600
per hour
Online Classes
With over 15 years of dedicated teaching experience, I am an accomplished and qualified educator specializing in Spoken English, Math, Science, Social Science, and Kannada Language. My expertise extends across various educational boards, including CBSE, ICSE, and state boards. Passionate about unraveling the mysteries of mathematical problems and chemical equations. I have garnered recognition with the prestigious Best Teacher Award for orchestrating state-level Science exams. Having contributed my skills to the esteemed MaxMuller Public School in Bangalore, I am committed to fostering a nurturing and inspiring learning environment. Join me on this educational journey where knowledge meets enthusiasm!
Enrolled my 10-year-old for math tutoring, and the improvement is remarkable. The tutor identifies weak spots quickly, like multiplication tables. Fun drills with timers make practice competitive and enjoyable. She explains errors without blame, turning mistakes into lessons. Custom worksheets align with his CBSE curriculum spot-on. Confidence boost evident; he volunteers answers in class now. Test scores rose steadily over two months. Responsive to parent queries, even on weekends. Affordable rates for such quality one-on-one attention. Planning long-term enrollment—excellent choice!
Super Tutor
Katira Maharaja Hata, Arrah
4 yrs of
Exp
24 students
1769 hrs of classes completed
700
per hour
Online Classes
Tutor's home
I've been teaching Class 10th students of schools from India and abroad. I primarily work with them to prepare for Olympiad, JEE foundation and school exams. I've been teaching students of class 8th-10th Science and Mathematics for more than 3 years. So far, I have taught more than 100 students from India and abroad. I teach international students Mathematics, Physics and Chemistry. I teach almost all boards of India such as CBSE, ICSE and state boards. I also teach IGCSE and IB students. I've my offline coaching institute where I am teaching students of CBSE and state boards who require help in Science and Mathematics. Fee displayed on my profile is for 1Ă—1 classes. For group classes, the fee is substantially reduced.
Find more Tutor for Real numbers in your City
- Delhi Mathematics Tutors
- Bangalore Mathematics Tutors
- Hyderabad Mathematics Tutors
- Chennai Mathematics Tutors
- Kolkata Mathematics Tutors
- Mumbai Mathematics Tutors
- Noida Mathematics Tutors
- Pune Mathematics Tutors
- Gurgaon Mathematics Tutors
- Lucknow Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Jaipur Mathematics Tutors
