# Number System: Aptitude Questions and Answers-6

#### Overview:

 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.

1. Find the smallest positive number which is exactly divisible by 3, 6, and 10?

1. 20
2. 30
3. 40
4. 50

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.

1. Find the LCM of 15, 20, 27?

1. 460
2. 480
3. 540
4. 560

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.

1. Find the LCM of $$\frac{8}{7}$$ and $$\frac{9}{5}$$?

1. 36
2. 49
3. 65
4. 72

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

1. Find the LCM of $$\frac{10}{7}$$, $$\frac{15}{4}$$, and $$\frac{18}{11}$$?

1. 60
2. 80
3. 90
4. 120

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

1. Which of the following is the LCM of 25, $$\frac{15}{7}$$, and 20?

1. 150
2. 180
3. 280
4. 300

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

1. 150 is the LCM of, which of the following numbers of a group?

1. 25, 15, 10, 5
2. 20, 15, 10, 5
3. 25, 20, 15, 10
4. 15, 12, 10, 5

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

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

1. Find the LCM of 56, 78, 99?

1. 72056
2. 72072
3. 76210
4. 78520

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.$$= 2^{3} \times 3^{2} \times 7^{1} \times 11^{1} \times 13^{1}$$ $$= 8 \times 9 \times 7 \times 11 \times 13 = 72072$$

1. 180 is the LCM of, which of the following numbers of a group?

1. 5, 12, 16, 45
2. 9, 15, 18, 60
3. 15, 18, 25, 50
4. 10, 15, 20, 25

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

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

1. Which of the following is the LCM of $$\frac{10}{9}$$, 9, and $$\frac{3}{10}$$?

1. 60
2. 90
3. 100
4. 120

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

1. Find the LCM of 35, 40, and 50?

1. 900
2. 1200
3. 1400
4. 1500

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.$$= 2^{3} \times 5^{2} \times 7^{1}$$ $$= 8 \times 25 \times 7 = 1400$$