What is the difference between HCF and LCM?

HCF (Highest Common Factor) is the largest number that divides two or more numbers exactly. LCM (Lowest Common Multiple) is the smallest number that is a multiple of two or more numbers. For example, HCF of 12 and 18 is 6, while LCM of 12 and 18 is 36.

How many questions are in this Playing with Numbers worksheet?

There are 60 questions divided into three levels — Level 1 (basic concepts), Level 2 (calculations and procedures), Level 3 (word problems and reasoning). All questions include step-by-step answers.

No. A prime number must have exactly two distinct factors: 1 and itself. The number 1 has only one factor (1), so it is neither prime nor composite. The smallest prime number is 2.

Worksheets

Playing with Numbers Class 6 CBSE Worksheet Free PDF Download with Answers

Sharpen your skills in factors, multiples, prime factorisation, divisibility tests, HCF and LCM with 60 graded questions and full solutions.

CBSEClass 6

SparkEd Team4 April 20267 min read

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45 practice questions across 3 difficulty levels with complete answer keys. Printable A4 format, perfect for revision!

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Why This Chapter Is a Game-Changer

$Playing with Numbers is probably the most fun chapter in Class 6 Maths. You get to break numbers apart, test divisibility rules like a detective, and find hidden relationships between numbers using HCF and LCM.$

$But it is also one of the most useful. HCF and LCM show up in fractions (finding common denominators), in ratio and proportion, and even in real-life problems like scheduling and packaging. Students who master this chapter find fractions much easier.$

$This Playing with Numbers Class 6 worksheet has 60 questions across three levels. Answers are included for every single question.$

What Does This Worksheet Cover?

$Aligned with NCERT Class 6 Chapter 3:$

$\text{HCF} \times \text{LCM} = \text{Product of the two numbers}$

$Level$	$Focus$	$Count$
$Level 1$	$Identify factors, multiples, primes, divisibility checks$	$20$
$Level 2$	$Prime factorisation, HCF, LCM calculations$	$20$
$Level 3$	$Word problems, combined HCF-LCM, tricky divisibility$	$20$

Sample Questions

$Level 1 — Warm Up$

$1. List all factors of 36. 2. Is 91 a prime or composite number? Explain. 3. Test whether 4,572 is divisible by 6.$

$Level 2 — Build Confidence$

$4. Find the prime factorisation of 180 using a factor tree. 5. Find the HCF of 48 and 72. 6. Find the LCM of 15, 20 and 30.$

$Level 3 — Push Yourself$

$7. Two bells ring at intervals of 12 minutes and 18 minutes. If they ring together at 9:00 AM, when will they ring together again? 8. Find the greatest number that divides both 120 and 150, leaving remainders of 4 and 6 respectively. 9. The HCF of two numbers is 12 and their LCM is 180. If one number is 36, find the other.$

Download Practice Playing with Numbers Online worksheet | 45 questions with answer key

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Tips and Common Mistakes

$1. Remember: 1 is neither prime nor composite. This is a classic exam question. Primes have exactly two factors. 1 has only one factor (itself).$

$2. Use divisibility rules to save time. Instead of dividing, check: if the last digit is even, it is divisible by 2. If the sum of digits is divisible by 3, the number is divisible by 3. Learn all the rules — they speed up prime factorisation too.$

$3. Do not confuse HCF and LCM. HCF is the greatest common factor (always smaller or equal). LCM is the smallest common multiple (always larger or equal). A quick check: HCF of two numbers can never be greater than either number.$

$\text{HCF} \times \text{LCM}$

$5. Word problems need careful reading. "Bells ring together again" means LCM. "Greatest number that divides" means HCF. Learn to spot these patterns.$