Quantitative Aptitudeमात्रात्मक योग्यता · महत्तम समापवर्तक और लघुत्तम समापवर्त्य

HCF and LCMमहत्तम समापवर्तक और लघुत्तम समापवर्त्य questions and answersप्रश्न और उत्तर

HCF and LCM word problems hide a simple question: are we cutting things into equal pieces (HCF) or waiting for things to line up again (LCM)?

Unlimitedअसीमित fresh questionsनए प्रश्न
Answersउत्तर always one tap awayहमेशा एक टैप दूर
1 subtopicउप-टॉपिक
SSC CGL ~1
TCS NQT ~1

Practice questions are in English for now.अभ्यास के प्रश्न अभी अंग्रेज़ी में हैं।

How hcf and lcm worksमहत्तम समापवर्तक और लघुत्तम समापवर्त्य को समझिए

Use HCF for “largest size that divides exactly”: the biggest tile, the longest tape, the largest group.

Use LCM for “when will they coincide”: bells ringing together, runners meeting at the start, the smallest number divisible by several numbers.

For two numbers, HCF × LCM equals their product. That one fact answers many questions.

Tricks that save timeसमय बचाने वाली ट्रिक्स

All tricks →सभी ट्रिक्स →

Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।

Formulaसूत्र✓ Checked on 1,005 cases✓ 1,005 मामलों पर जाँची गई

Same remainder → HCF of the differences

Use it when:कब इस्तेमाल करें: “Find the greatest number that divides 43, 91 and 183 leaving the same remainder.”

Subtract the numbers pairwise: 91 − 43, 183 − 91.
The answer is the HCF of the differences.

Exampleउदाहरण

43, 91, 183

→ HCF(48, 92) = 4

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: If a and b leave the same remainder when divided by d, then d divides b − a; the largest such d is the HCF of all the differences.

Limits:सीमाएँ: Only for “the same remainder”. For different given remainders, subtract each remainder from its number first.

Solved examplesहल किए गए उदाहरण

Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।

Example 1उदाहरण 1 · HCF and LCM word problems · Easyआसान
Three temple bells in Varanasi ring at intervals of 9, 8, 6 seconds. If they ring together now, after how many seconds will they next ring together?
1. 54 seconds
2. 65 seconds
3. 72 seconds
4. 79 seconds
Answer:उत्तर: 72 seconds
1. LCM(9, 8) = 72.
2. LCM with 6 = 72.
3. They ring together after 72 seconds.
Example 2उदाहरण 2 · HCF and LCM word problems · Mediumमध्यम
Three pieces of cloth at a shop in Surat measure 165 cm, 30 cm, 135 cm. What is the greatest length (in cm) of a measuring stick that can measure all three exactly?
1. 14 cm
2. 15 cm
3. 17 cm
4. 19 cm
Answer:उत्तर: 15 cm
1. HCF(165, 30) = 15.
2. HCF with 135 = 15.
Example 3उदाहरण 3 · HCF and LCM word problems · Hardकठिन
Find the greatest number that divides 224, 84, 63 leaving remainders 4, 4, 3 respectively.
1. 10
2. 15
3. 20
4. 25
Answer:उत्तर: 20
1. Exact multiples: 220, 80, 60.
2. HCF = 20.
Example 4उदाहरण 4 · HCF and LCM word problems · Mediumमध्यम
Three pieces of cloth at a shop in Surat measure 189 cm, 231 cm, 42 cm. What is the greatest length (in cm) of a measuring stick that can measure all three exactly?
1. 16 cm
2. 17 cm
3. 21 cm
4. 26 cm
Answer:उत्तर: 21 cm
1. HCF(189, 231) = 21.
2. HCF with 42 = 21.
Example 5उदाहरण 5 · HCF and LCM word problems · Mediumमध्यम
Three pieces of cloth at a shop in Surat measure 99 cm, 121 cm, 77 cm. What is the greatest length (in cm) of a measuring stick that can measure all three exactly?
1. 8 cm
2. 9 cm
3. 11 cm
4. 13 cm
Answer:उत्तर: 11 cm
1. HCF(99, 121) = 11.
2. HCF with 77 = 11.
Example 6उदाहरण 6 · HCF and LCM word problems · Mediumमध्यम
Three pieces of cloth at a shop in Surat measure 216 cm, 168 cm, 264 cm. What is the greatest length (in cm) of a measuring stick that can measure all three exactly?
1. 19 cm
2. 24 cm
3. 26 cm
4. 29 cm
Answer:उत्तर: 24 cm
1. HCF(216, 168) = 24.
2. HCF with 264 = 24.

Common mistakesआम गलतियाँ

Using LCM where HCF is needed (and the other way round).
Forgetting to add the remainder after finding the LCM.

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न

When do I use HCF and when LCM?

HCF for splitting into the largest equal parts; LCM for finding when events repeat together.

What is the relation between HCF and LCM?

For two numbers, HCF × LCM = the product of the numbers.

How do I find the HCF of fractions?

HCF of the numerators divided by the LCM of the denominators.