Least Common Multiple (LCM) of 169 and 122
The least common multiple (LCM) of 169 and 122 is 20618.
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 169 and 122?
First, calculate the GCD of 169 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 122 = 1 remainder 47 |
| 2 | 122 ÷ 47 = 2 remainder 28 |
| 3 | 47 ÷ 28 = 1 remainder 19 |
| 4 | 28 ÷ 19 = 1 remainder 9 |
| 5 | 19 ÷ 9 = 2 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 70 | 70 |
| 54 and 119 | 6426 |
| 116 and 117 | 13572 |
| 20 and 154 | 1540 |
| 179 and 16 | 2864 |