Least Common Multiple (LCM) of 106 and 168
The least common multiple (LCM) of 106 and 168 is 8904.
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 106 and 168?
First, calculate the GCD of 106 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 168 = 0 remainder 106 |
| 2 | 168 ÷ 106 = 1 remainder 62 |
| 3 | 106 ÷ 62 = 1 remainder 44 |
| 4 | 62 ÷ 44 = 1 remainder 18 |
| 5 | 44 ÷ 18 = 2 remainder 8 |
| 6 | 18 ÷ 8 = 2 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 23 | 552 |
| 38 and 72 | 1368 |
| 89 and 112 | 9968 |
| 99 and 107 | 10593 |
| 197 and 113 | 22261 |