Govt Exams
HCF × LCM = Product of numbers. 18 × 324 = 36 × other.
Therefore, other = 5832 ÷ 36 = 162.
16 = 2⁴, 24 = 2³ × 3, 36 = 2² × 3². LCM = 2⁴ × 3² = 16 × 9 = 144.
56 = 2³ × 7, 84 = 2² × 3 × 7, 140 = 2² × 5 × 7.
Common prime factors: 2 × 7 = 14.
Let numbers be 4k and 5k. HCF = k = 6.
Therefore, numbers are 24 and 30.
The larger number is 30.
12 = 2² × 3, 15 = 3 × 5, 20 = 2² × 5. LCM = 2² × 3 × 5 = 60.
This is the smallest number divisible by all three.
For co-prime numbers, HCF = 1.
Using HCF × LCM = Product: 1 × 221 = Product.
Therefore, product = 221.
144 = 2⁴ × 3². 196 = 2² × 7².
Common prime factors: 2².
Therefore, HCF = 4.
Using HCF × LCM = Product of two numbers: 15 × 180 = 45 × other number.
Therefore, other number = 2700 ÷ 45 = 60.
20 = 2² × 5, 30 = 2 × 3 × 5. LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60.
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.