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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, 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।

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

A

127127

B

167167

C

227227

D

247247

✓

Correct Answerसही उत्तर

D. 247D. 247

Explanationव्याख्या

Since the remainder is the same (7) in each case, first find the LCM of 12, 16, and 20.
12 = 2² × 3
16 = 2⁴
20 = 2² × 5
Therefore,
LCM = 2⁴ × 3 × 5 = 240
Now add the common remainder 7:
Required number = 240 + 7 = 247

चूँकि प्रत्येक स्थिति में शेषफल 7 समान है, इसलिए पहले 12, 16 और 20 का LCM ज्ञात करेंगे।

12 = 2² × 3
16 = 2⁴
20 = 2² × 5

अतः,

LCM = 2⁴ × 3 × 5 = 240

अब इसमें शेषफल 7 जोड़ेंगे:

अभीष्ट संख्या = 240 + 7 = 247

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