# H.C.F. and L.C.M.

1) The H.C.F. of $$\frac{9}{4},\frac{3}{20},\frac{9}{10} and \frac{15}{16}$$ is:

A) $$\frac{3}{80}$$ B) $$\frac{3}{2}$$ C) $$\frac{1}{40}$$ D) $$\frac{45}{2}$$

2) The L.C.M. of $$\frac{2}{3},\frac{3}{20},\frac{9}{10} and \frac{15}{16}$$ is:

A) $$\frac{3}{80}$$ B) $$\frac{3}{2}$$ C) $$\frac{1}{15}$$ D) $$\frac{45}{2}$$

3) The H.C.F. of 1.26, 1.155, 0.21 and 0.315 is:

A) 0.05 B) 0.105 C) 1.05 D) 0.03 E) 0.035 F) 0.005

4) The L.C.M. of 1.26, 1.155 and 0.21 is:

A) 0.132 B) 0.01386 C) 13.86 D) 1.386

5) The H.C.F. of $$\frac{12}{35}$$ and 4 is:

A) 3 B) $$\frac{12}{35}$$ C) $$\frac{35}{3}$$ D) $$\frac{4}{35}$$

6) Let a and b are two positive numbers such that a-b=9 and the H.C.F. and L.C.M. of the numbers are 3 and 120 respectively, then $$\frac{a}{b}$$ is equal to:

A) $$\frac{40}{9}$$ B) $$\frac{8}{5}$$ C) 20 D) 4

*Note**: –** H.C.F. means Highest Common Factor or Greatest Common Divisor (g.c.d.) and L.C.M. means Least Common Multiple.*

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**Answers and explanations****:**

**1)** A) $$\frac{3}{80}.$$

**Explanation****:-**

H.C.F. of fraction = H.C.F. of numerators / L.C.M. of denominators.

**2)** D) $$\frac{45}{2}.$$

**Explanation****:-**

L.C.M. of fractions = L.C.M. of numerators / H.C.F. of denominators.

**3)** B) 0.105.

**Explanation****:-**

Given numbers are 1.26, 1.155, 0.21 and 0.315.

H.C.F. of 1260, 1155, 210 and 315 is 105.

Hence H.C.F. 1.26, 1.155, 0.21 and 0.315 = 0.105.

**4)** C) 13.86.

**Explanation****:-**

Given numbers are 1.26, 1.155 and 0.21.

L.C.M. of 1260, 1155 and 210 is 13860.

Hence L.C.M. 1.26, 1.155 and 0.21 = 13.86.

**5)** D) $$\frac{4}{35}.$$

**6)** B) $$\frac{8}{5}.$$

**Explanation****:-**

a-b=9, ab=360,

$$(a+b)^2=(a-b)^2+4ab$$

$$\Rightarrow (a+b)^2=(9)^2+4.360$$

$$\Rightarrow (a+b)^2=81+1440$$

$$\Rightarrow (a+b)^2=1521$$

$$\Rightarrow (a+b)=39$$

Hence a=24, b=15.