Questions and Answers Type: | MCQ (Multiple Choice Questions). |

Main Topic: | Quantitative Aptitude. |

Quantitative Aptitude Sub-topic: | Number System Aptitude Questions and Answers. |

Number of Questions: | 10 Questions with Solutions. |

- Find the smallest positive number which is exactly divisible by 3, 6, and 10?
- 20
- 30
- 40
- 50

Answer: (b) 30

Solution:

Solution:

**Step(1):** Factorize the numbers into their prime factors.$$ 3 = 3^{1} $$ $$ 6 = 2^{1} \times 3^{1} $$ $$ 10 = 2^{1} \times 5^{1} $$ **Step(2):** Collect all the distinct factors with their maximum available power.$$ = 2^{1}, \ 3^{1}, \ 5^{1} $$ **Step(3):** Multiply the collected factors.$$ = 2 \times 3 \times 5 = 30 $$ Here, 30 is the smallest positive number which is exactly divisible by 3, 6, and 10.

- Find the LCM of 15, 20, 27?
- 460
- 480
- 540
- 560

Answer: (c) 540

Solution:

Solution:

**Step(1):** Factorize the numbers into their prime factors.$$ 15 = 3 \times 5 = 3^{1} \times 5^{1} $$ $$ 20 = 2 \times 2 \times 5 = 2^{2} \times 5^{1} $$ $$ 27 = 3 \times 3 \times 3 = 3^{3} $$ **Step(2):** Collect all the distinct factors with their maximum available power.$$ = 2^{2}, \ 3^{3}, \ 5^{1} $$ **Step(3):** Multiply the collected factors.$$ = 2^{2} \times 3^{3} \times 5^{1} $$ $$ = 4 \times 27 \times 5 = 540 $$ Here, 540 is the smallest positive number which is exactly divisible by 15, 20, and 27.

- Find the LCM of \(\frac{8}{7}\) and \(\frac{9}{5}\)?
- 36
- 49
- 65
- 72

Answer: (d) 72

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (8,9)}{HCF \ of \ (7,5)} $$ $$ = \frac{72}{1} = 72 $$

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (8,9)}{HCF \ of \ (7,5)} $$ $$ = \frac{72}{1} = 72 $$

- Find the LCM of \(\frac{10}{7}\), \(\frac{15}{4}\), and \(\frac{18}{11}\)?
- 60
- 80
- 90
- 120

Answer: (c) 90

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (10, 15, 18)}{HCF \ of \ (7, 4, 11)} $$ $$ = \frac{90}{1} = 90 $$

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (10, 15, 18)}{HCF \ of \ (7, 4, 11)} $$ $$ = \frac{90}{1} = 90 $$

- Which of the following is the LCM of 25, \(\frac{15}{7}\), and 20?
- 150
- 180
- 280
- 300

Answer: (d) 300

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (25, 15, 20)}{HCF \ of \ (1, 7, 1)} $$ $$ = \frac{300}{1} = 300 $$

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (25, 15, 20)}{HCF \ of \ (1, 7, 1)} $$ $$ = \frac{300}{1} = 300 $$

- 150 is the LCM of, which of the following numbers of a group?
- 25, 15, 10, 5
- 20, 15, 10, 5
- 25, 20, 15, 10
- 15, 12, 10, 5

Answer: (a) 25, 15, 10, 5

Solution: 150 is the LCM of 25, 15, 10, 5.

Solution: 150 is the LCM of 25, 15, 10, 5.

- Find the LCM of 56, 78, 99?
- 72056
- 72072
- 76210
- 78520

Answer: (b) 72072

Solution:

Solution:

**Step(1):** Factorize the numbers into their prime factors.$$ 56 = 2 \times 2 \times 2 \times 7 = 2^{3} \times 7^{1} $$ $$ 78 = 2 \times 3 \times 13 = 2^{1} \times 3^{1} \times 13^{1} $$ $$ 99 = 3 \times 3 \times 11 = 3^{2} \times 11^{1} $$ **Step(2):** Collect all the distinct factors with their maximum available power.$$ = 2^{3}, \ 3^{2}, \ 7^{1} \ 11^{1} \ 13^{1} $$ **Step(3):** Multiply the collected factors.$$ = 2^{3} \times 3^{2} \times 7^{1} \times 11^{1} \times 13^{1} $$ $$ = 8 \times 9 \times 7 \times 11 \times 13 = 72072 $$

- 180 is the LCM of, which of the following numbers of a group?
- 5, 12, 16, 45
- 9, 15, 18, 60
- 15, 18, 25, 50
- 10, 15, 20, 25

Answer: (b) 9, 15, 18, 60

Solution: 180 is the LCM of 9, 15, 18, 60.

Solution: 180 is the LCM of 9, 15, 18, 60.

- Which of the following is the LCM of \(\frac{10}{9}\), 9, and \(\frac{3}{10}\)?
- 60
- 90
- 100
- 120

Answer: (b) 90

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (10, 9, 3)}{HCF \ of \ (9, 1, 10)} $$ $$ = \frac{90}{1} = 90 $$

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (10, 9, 3)}{HCF \ of \ (9, 1, 10)} $$ $$ = \frac{90}{1} = 90 $$

- Find the LCM of 35, 40, and 50?
- 900
- 1200
- 1400
- 1500

Answer: (c) 1400

Solution:

Solution:

**Step(1):** Factorize the numbers into their prime factors.$$ 35 = 5^{1} \times 7^{1} $$ $$ 40 = 2 \times 2 \times 2 \times 5 = 2^{3} \times 5^{1} $$ $$ 50 = 2 \times 5 \times 5 = 2^{1} \times 5^{2} $$ **Step(2):** Collect all the distinct factors with their maximum available power.$$ = 2^{3}, \ 5^{2}, \ 7^{1} $$ **Step(3):** Multiply the collected factors.$$ = 2^{3} \times 5^{2} \times 7^{1} $$ $$ = 8 \times 25 \times 7 = 1400 $$

Lec 1: Introduction to Number System
Lec 2: Factors of Composite Number
Questions and Answers-1
Lec 3: Basic Remainder Theorem
Questions and Answers-2
Lec 4: Polynomial Remainder Theorem
Questions and Answers-3
Questions and Answers-4
Questions and Answers-5
Lec 5: LCM of Numbers
Questions and Answers-6
Lec 6: HCF of Numbers
Questions and Answers-7
Questions and Answers-8
Lec 7: Divisibility Rules of Numbers
Questions and Answers-9
Questions and Answers-10
Questions and Answers-11
Questions and Answers-12
Questions and Answers-13
Questions and Answers-14
Questions and Answers-15
Questions and Answers-16
Questions and Answers-17
Questions and Answers-18
Questions and Answers-19
Questions and Answers-20