Least Common Multiple (LCM) of 106 and 169
The least common multiple (LCM) of 106 and 169 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 106 and 169?
First, calculate the GCD of 106 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 169 = 0 remainder 106 |
| 2 | 169 ÷ 106 = 1 remainder 63 |
| 3 | 106 ÷ 63 = 1 remainder 43 |
| 4 | 63 ÷ 43 = 1 remainder 20 |
| 5 | 43 ÷ 20 = 2 remainder 3 |
| 6 | 20 ÷ 3 = 6 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 65 | 12415 |
| 96 and 162 | 2592 |
| 160 and 48 | 480 |
| 109 and 195 | 21255 |
| 180 and 20 | 180 |