Least Common Multiple (LCM) of 168 and 122
The least common multiple (LCM) of 168 and 122 is 10248.
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 168 and 122?
First, calculate the GCD of 168 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 122 = 1 remainder 46 |
| 2 | 122 ÷ 46 = 2 remainder 30 |
| 3 | 46 ÷ 30 = 1 remainder 16 |
| 4 | 30 ÷ 16 = 1 remainder 14 |
| 5 | 16 ÷ 14 = 1 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 195 | 7410 |
| 107 and 154 | 16478 |
| 135 and 100 | 2700 |
| 55 and 16 | 880 |
| 169 and 135 | 22815 |