Math 9th Chap 4 : Topic 3 - Maryam Publications

Math Chapter 4 : Topic 3

Algebraic HCF and LCM

1 / 25

The highest common factor $(HCF)$ of algebraic expressions is:

A) The greatest expression that divides all given expressions exactly

B) The highest product of all terms

C) The largest sum of terms

D) The smallest common multiple

2 / 25

The least common multiple $(LCM)$ of algebraic expressions is:

A) The highest degree term only

B) The smallest factor

C) The expression with least variables

D) The smallest expression divisible by all given expressions

3 / 25

$HCF$ of ${6x}^{2}$ and $9x$ is:

A) $6x$

B) ${9x}^{2}$

C) $3x$

D) ${3x}^{2}$

4 / 25

$LCM$ of $(2x)$ and $({3x}^{2})$ is:

A) $6x$

B) ${5x}^{2}$

C) $3x$

D) ${6x}^{2}$

5 / 25

Which statement is correct?

A) $HCF \times LCM =$ product of expressions

B) $HCF + LCM =$ product

C) $HCF \div LCM =$ product

D) $HCF \times LCM =$ difference

6 / 25

$HCF$ of $x^{2}$ and $x^{3}$ is:

A) $x^{3}$

B) $x^{2}$

C) $x$

D) $1$

7 / 25

$LCM$ of $(x^{2})$ and $(x^{3})$ is:

A) $x^{2}$

B) $x$

C) $1$

D) $x^{3}$

8 / 25

$HCF$ of $({4x}^{2}y)$ and $({6xy}^{2})$ is:

A) ${12x}^{2}y^{2}$

B) $4xy$

C) $2xy$

D) ${2x}^{2}y^{2}$

9 / 25

$LCM$ of $(4x)$ and $({6x}^{2})$ is:

A) $2x$

B) $6x$

C) ${12x}^{2}$

D) ${4x}^{2}$

10 / 25

Which is always true?

A) $HCF$ is always zero

B) $HCF \leq LCM$

C) $HCF = LCM$ always

D) $HCF > LCM$

11 / 25

$HCF$ of $(ax)$ and $(bx)$ is:

A) $abx$

B) $x$

C) $ax + bx$

D) $(a + b)x$

12 / 25

$LCM$ of $(ax)$ and $(bx)$ is:

A) $x$

B) $(a + b)x$

C) ${abx}^{2}$

D) $abx$

13 / 25

If $HCF = 3x$ and $LCM = {12x}^{2}$, product of expressions is:

A) ${15x}^{2}$

B) ${36x}^{3}$

C) $9x$

D) $12x$

14 / 25

$HCF$ of $(x^{2} + x)$ is:

A) $1$

B) $x$

C) $x^{2}$

D) $x + 1$

15 / 25

$LCM$ of $(x(x + 1))$ and $(x(x + 2))$ includes:

A) $x(x + 1)(x + 2)$

B) $x^{2}$ only

C) $(x + 1)$ only

D) Only $x$

16 / 25

Which method is used for finding $HCF$ of algebraic expressions?

A) Addition

B) Graphing

C) Substitution

D) Factorization

17 / 25

$LCM$ is useful when:

A) Synchronizing events ($e.g.$, cycles)

B) Reducing numbers

C) Finding averages

D) Finding greatest value

18 / 25

$HCF$ of $({3x}^{2}y)$ and $({9xy}^{2})$ is:

A) $6xy$

B) ${3x}^{2}y^{2}$

C) ${9x}^{2}y^{2}$

D) $3xy$

19 / 25

$LCM$ of ${2x}^{2}$ and ${4x}^{3}$ is:

A) ${4x}^{3}$

B) ${8x}^{5}$

C) ${2x}^{2}$

D) ${6x}^{3}$

20 / 25

If two expressions are co-prime, their $HCF$ is:

A) Product

B) $LCM$

C) $1$

D) $0$

21 / 25

$HCF$ of $(5x)$ and $(7x)$ is:

A) $5x + 7x$

B) $35x$

C) $x$

D) $12x$

22 / 25

$LCM$ of $(x)$ and $(x^{2})$ is:

A) $x^{3}$

B) $x$

C) $1$

D) $x^{2}$

23 / 25

Which is correct relation?

A) $HCF \times LCM = sum$

B) $HCF + LCM =$ difference

C) $HCF \div LCM =$ product

D) $HCF \times LCM =$ product

24 / 25

$HCF$ helps in:

A) Simplifying fractions

B) Graphing functions

C) Expanding expressions

D) Increasing degree

25 / 25

$LCM$ of algebraic expressions is found by:

A) Adding terms

B) Taking smallest powers

C) Removing variables

D) Taking highest powers and coefficients

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