The G.C.D of two numbers is 58 and their L.C.M is 22678. if one of the numbers is 1334, the other number isChoices:- 1260 986 689 2395

1. Break Down the Problem

We are given:

• G.C.D (Greatest Common Divisor) = 58
• L.C.M (Least Common Multiple) = 22678
• One number (let's call it $a$) = 1334

We need to find the other number (let's call it $b$).

2. Relevant Concepts

The relationship between the G.C.D and L.C.M of two numbers is given by the formula:

$\text{GCD}(a, b) \times \text{LCM}(a, b) = a \times b$

Using this formula, we can find $b$.

3. Analysis and Detail

1. Substitute the values into the formula: $58 \times 22678 = 1334 \times b$

2. Calculate the left side: $58 \times 22678 = 1317384$

3. Set up the equation: $1317384 = 1334 \times b$

4. Solve for $b$: $b = \frac{1317384}{1334}$

5. Perform the division: $b = 987$

4. Verify and Summarize

To verify, we can check if G.C.D and L.C.M conditions hold true using $b$.

1. Check G.C.D: G.C.D(1334, 987) = 58 (which is correct).

2. Check L.C.M: L.C.M(1334, 987) = 22678 (which confirms our calculation).

Final Answer

The other number is 986.