Find the product of HCF and LCM of 1.08, 0.36 and 0.9.

Options

A. `0.999`
B. `1.009`
C. `0.900`
D. `0.972`

Answer

To find the product of the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of the numbers 1.08, 0.36, and 0.9, we can follow these steps:

### Step 1: Convert the decimal numbers to fractions
1.08 = 108/100
0.36 = 36/100
0.9 = 90/100

### Step 2: Simplify the fractions
- 1.08 = 27/25 (by dividing numerator and denominator by 4)
- 0.36 = 9/25 (by dividing numerator and denominator by 4)
- 0.9 = 9/10 (by dividing numerator and denominator by 10)

### Step 3: Find the HCF of the numerators and the LCM of the denominators
**Numerators:** 27, 9, 9
**Denominators:** 25, 25, 10

**HCF of 27, 9, 9:**
- The factors of 27 are 1, 3, 9, 27.
- The factors of 9 are 1, 3, 9.
- The common factors are 1, 3, 9.
- Therefore, HCF = 9.

**LCM of 25, 25, 10:**
- The multiples of 25 are 25, 50, 75, 100, 125, ...
- The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
- The least common multiple is 50.

### Step 4: Find the HCF and LCM of the original numbers
HCF = 9/25
LCM = 27/10

### Step 5: Calculate the product of HCF and LCM
Product = HCF × LCM
= (9/25) × (27/10)
= (9 × 27) / (25 × 10)
= 243 / 250

### Step 6: Final answer
The product of HCF and LCM of 1.08, 0.36, and 0.9 is **243/250**.

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