Least Common Multiple (LCM) of 169 and 106
The least common multiple (LCM) of 169 and 106 is 17914.
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 106?
First, calculate the GCD of 169 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 106 = 1 remainder 63 |
| 2 | 106 ÷ 63 = 1 remainder 43 |
| 3 | 63 ÷ 43 = 1 remainder 20 |
| 4 | 43 ÷ 20 = 2 remainder 3 |
| 5 | 20 ÷ 3 = 6 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 154 | 2156 |
| 127 and 81 | 10287 |
| 27 and 161 | 4347 |
| 123 and 12 | 492 |
| 186 and 102 | 3162 |