Least Common Multiple (LCM) of 198 and 169
The least common multiple (LCM) of 198 and 169 is 33462.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 198 and 169?
First, calculate the GCD of 198 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 169 = 1 remainder 29 |
| 2 | 169 ÷ 29 = 5 remainder 24 |
| 3 | 29 ÷ 24 = 1 remainder 5 |
| 4 | 24 ÷ 5 = 4 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 66 | 5478 |
| 123 and 14 | 1722 |
| 146 and 63 | 9198 |
| 77 and 85 | 6545 |
| 91 and 93 | 8463 |