The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
A. 276
B. 299
C. 322
D. 345
Answer: Option C
Solution(By Examveda Team)
The HCF of a group of numbers will be always a factor of their LCM.HCF is the product of all common prime factors using the least power of each common prime factor.
LCM is the product of highest powers of all prime factors.
Clearly, the numbers are (23 x 13) and (23 x 14)
∴ Larger number = (23 x 14) = 322
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Comments ( 3 )
Related Questions on Problems on H.C.F and L.C.M
Here Ratio of two numbers is given as 13:14 not exact number...now
1st no = 13× HCF = 13 × 23 = 299
2nd no = 14 × HCF = 14 × 23 = 322
Clearly , the larger no is 322 option C is correct
एचसीएफ प्रत्येक सामान्य अभाज्य गुणनखंड की न्यूनतम शक्ति का उपयोग करने वाले सभी सामान्य अभाज्य कारकों का उत्पाद है।
एलसीएम सभी प्रमुख कारकों की उच्चतम शक्तियों का उत्पाद है।
स्पष्ट रूप से, संख्याएँ (23 x 13) और (23 x 14) हैं।
बड़ी संख्या = (23 x 14) = 322
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