Quantitative Aptitude - MCQ Practice Questions

Using prime factorization: 48 = 2⁴ × 3, 64 = 2⁶. HCF = 2⁴ = 16 (taking lowest powers of common prime factors).

Prime factorization: 12 = 2² × 3, 18 = 2 × 3². LCM = 2² × 3² = 4 × 9 = 36 (taking highest powers of all prime factors).

This question asks us to find the Highest Common Factor (HCF) of two numbers using prime factorization or the Euclidean algorithm.

Step 1: Prime factorization of 56

Express 56 as a product of prime numbers.

Step 2: Prime factorization of 72

Express 72 as a product of prime numbers.

Step 3: Find the HCF

The HCF is the product of common prime factors with their lowest powers.

The HCF of 56 and 72 is 8, making the correct answer (B).

This question asks us to find the Least Common Multiple (LCM) of two numbers using prime factorization.

Step 1: Find prime factorization of 15

Break 15 into its prime factors.

Step 2: Find prime factorization of 25

Break 25 into its prime factors.

Step 3: Calculate LCM using highest powers of all prime factors

The LCM is found by taking the highest power of each prime that appears in either factorization: 3¹ and 5².

The LCM of 15 and 25 is 75.

36 = 2² × 3², 48 = 2⁴ × 3. HCF = 2² × 3 = 12, LCM = 2⁴ × 3² = 144.

Product = 36 × 48 = HCF × LCM = 12 × 144 = 1728.

Using formula: HCF × LCM = Product of two numbers. 8 × 96 = 24 × x. 768 = 24x. x = 32.

100 = 2² × 5², 150 = 2 × 3 × 5², 200 = 2³ × 5².

Common factors: 2¹ × 5² = 2 × 25 = 50.

This question asks us to find the least common multiple (LCM) of two numbers using prime factorization.

Step 1: Find prime factorization of 84

Break 84 into its prime factors by dividing by smallest primes.

Step 2: Find prime factorization of 140

Break 140 into its prime factors by dividing by smallest primes.

Step 3: Calculate LCM using highest powers of all prime factors

LCM is found by taking the highest power of each prime factor that appears in either number.

The LCM of 84 and 140 is 420, which is option (A).

Need to find LCM of 8, 12, 16. 8 = 2³, 12 = 2² × 3, 16 = 2⁴. LCM = 2⁴ × 3 = 48 minutes.

So they ring again at 12:00 + 48 min = 12:48 PM.

Let numbers be 12a and 12b where HCF(a,b)=1. LCM = 12ab = 240, so ab = 20.

Numbers: 12a and 12b with |12a - 12b| = 12, so |a - b| = 1.

If a=4, b=5: numbers are 48 and 60.

Check: 48-60 = -12 (difference is 12).

Using the formula: HCF × LCM = Product of two numbers.

Therefore, 12 × LCM = 2160, so LCM = 2160 ÷ 12 = 180.

Factors of 18: 1, 2, 3, 6, 9, 18.

Factors of 27: 1, 3, 9, 27.

Common factors: 1, 3, 9.

Highest common factor = 9.

20 = 2² × 5, 30 = 2 × 3 × 5. LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60.

Using HCF × LCM = Product of two numbers: 15 × 180 = 45 × other number.

Therefore, other number = 2700 ÷ 45 = 60.

144 = 2⁴ × 3². 196 = 2² × 7².

Common prime factors: 2².

Therefore, HCF = 4.

For co-prime numbers, HCF = 1.

Using HCF × LCM = Product: 1 × 221 = Product.

Therefore, product = 221.

12 = 2² × 3, 15 = 3 × 5, 20 = 2² × 5. LCM = 2² × 3 × 5 = 60.

This is the smallest number divisible by all three.

Let numbers be 4k and 5k. HCF = k = 6.

Therefore, numbers are 24 and 30.

The larger number is 30.

56 = 2³ × 7, 84 = 2² × 3 × 7, 140 = 2² × 5 × 7.

Common prime factors: 2 × 7 = 14.

16 = 2⁴, 24 = 2³ × 3, 36 = 2² × 3². LCM = 2⁴ × 3² = 16 × 9 = 144.