Least Common Multiple (LCM) of 163 and 121
The least common multiple (LCM) of 163 and 121 is 19723.
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 163 and 121?
First, calculate the GCD of 163 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 121 = 1 remainder 42 |
| 2 | 121 ÷ 42 = 2 remainder 37 |
| 3 | 42 ÷ 37 = 1 remainder 5 |
| 4 | 37 ÷ 5 = 7 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 129 | 11481 |
| 136 and 20 | 680 |
| 193 and 38 | 7334 |
| 100 and 163 | 16300 |
| 83 and 92 | 7636 |