Home › Questions › Math › HCF AND LCM

RailwaysSSCMathHCF AND LCMMedium

HCF AND LCM practice question for Railways, SSC. Review the correct answer and explanation, then continue with related practice below.

Question language / प्रश्न भाषा

Find the least number which when divided by 12, 15 and 20 leaves remainder 7 in each case.

वह सबसे छोटी संख्या ज्ञात कीजिए जिसे 12, 15 और 20 से भाग देने पर प्रत्येक बार 7 शेष बचे।

Answer and explanation are free to read — no sign-in required.उत्तर और व्याख्या पढ़ने के लिए साइन-इन आवश्यक नहीं है।

A

5757

B

6060

C

6767

✓

D

127127

Correct Answerसही उत्तर

C. 67C. 67

Explanationव्याख्या

Since the remainder is the same (7) in each case, subtract 7 from the required number.
The resulting number must be exactly divisible by 12, 15, and 20.
So, find:
LCM of 12, 15, and 20
Prime factorization:
12 = 2² × 3
15 = 3 × 5
20 = 2² × 5
Therefore,
LCM = 2² × 3 × 5 = 60
Now add the common remainder:
Required number = 60 + 7 = 67

चूँकि प्रत्येक स्थिति में समान शेषफल 7 है, इसलिए पहले 12, 15 और 20 का LCM ज्ञात करेंगे।

12 = 2² × 3
15 = 3 × 5
20 = 2² × 5

अतः,

LCM = 2² × 3 × 5 = 60

अब इसमें शेषफल 7 जोड़ेंगे:

अभीष्ट संख्या = 60 + 7 = 67

Try the Quiz Containing This Question

Attempt this question in its original quiz and continue with the complete test.

HCF and LCM Practice Set – 30 Questions →

Practice More Like This

Vitorr selects questions using the same topic, subject, exam and overlapping concepts—not just database order.

Start 10-Question Related Practice →View All HCF AND LCM Questions

प्रश्न 20 Find the least number greater than the divisors which leaves remainder 5 when divided by 8, 12 and 16. वह सबसे छोटी संख्या ज्ञात कीजिए जो भाजकों से बड़ी हो तथा 8, 12 और 16 से भाग देने पर 5 शेष छोड़े।Same topic · Same subject · Same exam

प्रश्न 19 Find the least number which when divided by 12, 15 and 20 leaves remainder 7 in each case. वह सबसे छोटी संख्या ज्ञात कीजिए जिसे 12, 15 तथा 20 से भाग देने पर प्रत्येक बार 7 शेष बचे।Same topic · Same subject · Same exam

Find the least number which when divided by 12, 16 and 20 leaves remainder 7 in each case.वह सबसे छोटी संख्या ज्ञात कीजिए जिसे 12, 16 और 20 से भाग देने पर प्रत्येक बार 7 शेष बचे।Same topic · Same subject · Same exam

What is the smallest number which when divided by 16, 20 and 24 leaves remainder 5 in each case?वह सबसे छोटी संख्या क्या है जिसे 16, 20 और 24 से भाग देने पर प्रत्येक बार 5 शेष बचे?Same topic · Same subject · Same exam

Find the greatest number which divides 615 and 963 leaving remainder 6 in each case.वह सबसे बड़ी संख्या ज्ञात कीजिए जो 615 और 963 को भाग देने पर प्रत्येक बार 6 शेष छोड़े।Same topic · Same subject · Same exam

Find the greatest number that divides 110, 170 and 230 leaving the same remainder in each case.वह सबसे बड़ी संख्या ज्ञात कीजिए जो 110, 170 और 230 को भाग देने पर प्रत्येक बार समान शेषफल छोड़े।Same topic · Same subject · Same exam

Related Quizzes

Continue with quizzes connected to HCF AND LCM and Math. Sign up is required only when you start a quiz.

SSC CGL Tough Mathematics Practice Set 11 – 25 Questions | 15 MinutesOpen quiz →SSC CGL Tough Mathematics Practice Set 1 – 25 Bilingual QuestionsOpen quiz →UPSC CSAT 2027 Tough Practice Quiz Set 001 – Maths, Logic & Analytical ReasoningOpen quiz →15 mins SSC Maths Set 18Open quiz →

Related Study Material

HCF and LCM Practice QuestionsRead study article →Mathematics Practice Set — 30 Questions गणित अभ्यास सेट — 30 प्रश्नRead study article →15 mins SSC Maths Set 18 SolutionRead study article →