Least Common Multiple (LCM) of 197 and 162
The least common multiple (LCM) of 197 and 162 is 31914.
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 197 and 162?
First, calculate the GCD of 197 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 162 = 1 remainder 35 |
| 2 | 162 ÷ 35 = 4 remainder 22 |
| 3 | 35 ÷ 22 = 1 remainder 13 |
| 4 | 22 ÷ 13 = 1 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 87 | 7134 |
| 112 and 35 | 560 |
| 120 and 81 | 3240 |
| 116 and 92 | 2668 |
| 58 and 102 | 2958 |