Least Common Multiple (LCM) of 168 and 106
The least common multiple (LCM) of 168 and 106 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 168 and 106?
First, calculate the GCD of 168 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 106 = 1 remainder 62 |
| 2 | 106 ÷ 62 = 1 remainder 44 |
| 3 | 62 ÷ 44 = 1 remainder 18 |
| 4 | 44 ÷ 18 = 2 remainder 8 |
| 5 | 18 ÷ 8 = 2 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 189 | 7749 |
| 196 and 127 | 24892 |
| 109 and 75 | 8175 |
| 48 and 60 | 240 |
| 161 and 93 | 14973 |