Least Common Multiple (LCM) of 172 and 198
The least common multiple (LCM) of 172 and 198 is 17028.
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 172 and 198?
First, calculate the GCD of 172 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 198 = 0 remainder 172 |
| 2 | 198 ÷ 172 = 1 remainder 26 |
| 3 | 172 ÷ 26 = 6 remainder 16 |
| 4 | 26 ÷ 16 = 1 remainder 10 |
| 5 | 16 ÷ 10 = 1 remainder 6 |
| 6 | 10 ÷ 6 = 1 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 65 | 10920 |
| 156 and 151 | 23556 |
| 70 and 55 | 770 |
| 69 and 125 | 8625 |
| 128 and 145 | 18560 |