| Direction: Q. 1 to 5 |
| Divisibility Rules |
| HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM. |
| {Product of numbers = \[HCF\times LCM\]} |
| Based on the above information answer the following questions. |
| If two positive integers a and b are expressible in terms of primes as \[a={{p}^{2}}{{q}^{4}}\] and\[b={{p}^{3}}{{q}^{2}}\], then which of the following is true? |
A) \[HCF=p{{q}^{2}}\times LCM\]
B) \[LCM=p{{q}^{2}}\times HCF\]
C) \[LCM={{p}^{2}}q\times HCF\]
D) \[HCF={{p}^{2}}q\times LCM\]
Correct Answer: B
Solution :
| (i) The factors are |
| \[a={{p}^{2}}{{q}^{4}}\] |
| \[b={{p}^{3}}{{q}^{2}}\] |
| HCF of a and \[b={{p}^{2}}{{q}^{2}}\] |
| LCM of a and \[b={{p}^{3}}{{q}^{4}}\] |
| \[\therefore \,\,LCM=p{{q}^{2}}\times HCF\] |
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