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Find the least common multiple of 198 and 44.

The least common multiple of 198 and 44 is _________.

(Type a whole number.)

Answer :

To find the least common multiple (LCM) of 198 and 44, we can use the relationship between the greatest common divisor (GCD) and the LCM. Here's a step-by-step guide to solving this problem:

1. Understand the Relationship: The LCM of two numbers can be found using the formula:
[tex]\[
\text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)}
\][/tex]
where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are the two numbers.

2. Find the GCD: First, we need to determine the greatest common divisor of 198 and 44. The GCD is the largest number that divides both numbers without leaving a remainder.

3. Calculate the GCD: In this case, the GCD of 198 and 44 is 22.

4. Apply the LCM Formula: Now, substitute the values into the LCM formula:
[tex]\[
\text{LCM}(198, 44) = \frac{|198 \times 44|}{22}
\][/tex]

5. Multiply the Numbers: Calculate the numerator:
[tex]\[
198 \times 44 = 8712
\][/tex]

6. Divide by the GCD: Now, divide the result by the GCD:
[tex]\[
\frac{8712}{22} = 396
\][/tex]

7. Conclusion: Therefore, the least common multiple of 198 and 44 is 396.

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