The HCF of two numbers is 13 and their LCM is 70 times their HCF. What will be the smaller number if one of the numbers is above 400 and both the numbers are greater than 13?
Correct Answer : c ) 26Explanation :
According to the question,
HCF of two numbers be 13
So, let us assume Ist number be 13a and the IInd number be 13b
Product of two numbers = LCM × HCF
13a × 13b = LCM × 13
According to the question, LCM is 70 times their HCF
⇒ 13a × 13b = 70 × 13 × 13
⇒ ab = 70
The factors of 70 are 2 × 5 × 7
If we consider a = 5 × 7 i.e. 35
Then, Ist number = 13 × 35 = 455 (number greater than 400)
And, IInd number = 13 × 2 = 26
Hence, (c) is the correct answer.
Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA, UP SI, etc.
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