LCM and HCF Questions and answers

Topics

21). Find the greatest 4 digit number which when divided by 15, 18, 21 and 27 leaves in each case a remainder 7.
 A). 9457 B). 9547 C). 9947 D). 9967
22). Which of the following fraction is the greatest?
$$\Large \frac{7}{8}$$, $$\Large \frac{6}{7}$$, $$\Large \frac{4}{5}$$, $$\Large \frac{5}{6}$$

 A). $$\Large \frac{6}{7}$$ B). $$\Large \frac{5}{6}$$ C). $$\Large \frac{4}{5}$$ D). $$\Large \frac{7}{8}$$
23). A number when divided by 32 leaves the remainder 29. This number when divided by 8 will leave the remainder
 A). 3 B). 5 C). 7 D). 29
24). A number lying between 1000 and 2000 is such that on division by 2, 3, 4, 5, 6, 7 and 8 leaves remainder respectively 1, 2, 3, 4, 5, 6 and 7. The number is
 A). 1876 B). 1679 C). 1778 D). 1654
25). Three persons begin to walk around a circular track. They complete their revolutions in $$\Large 15\frac{1}{6}\ secs., 16\frac{1}{4}] secs.\ and\ 18\frac{2}{3}\ secs.$$ rerspectively. After what time will they be together at the starting point again?
 A). $$\Large 303\frac{1}{3}$$ secs. B). 364 secs. C). 3604 secs, D). 3640 secs.

26). The greatest number, which divides 171, and 251 leaving remainders 3 and 6 respectively is
 A). 3 B). 5 C). 7 D). 15
27). The HCF of two positive integers is 5 and their LCM is 105. The numbers are
 A). 5, 105 B). 15, 35 C). 5, 105 or 15, 35 D). None of these
28). The LCM of $$\Large x^{3}-1$$, $$\Large x^{2}-1$$ and $$\Large \left(x-1\right)^{2}$$ is
 A). $$\Large \left(x+1\right) \left(x-1\right) \left(x^{2}+x+1\right)$$ B). $$\Large \left(x+1\right)^{2} \left(x-1\right) \left(x^{2}-x+1\right)$$ C). $$\Large \left(x-1\right)^{2} \left(x-1\right) \left(x^{2}+x+1\right)$$ D). $$\Large \left(x-1\right)^{2} \left(x+1\right) \left(x^{2}-x+1\right)$$
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