Least Common Multiple (LCM) of 106 and 137
The least common multiple (LCM) of 106 and 137 is 14522.
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 137?
First, calculate the GCD of 106 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 137 = 0 remainder 106 |
| 2 | 137 ÷ 106 = 1 remainder 31 |
| 3 | 106 ÷ 31 = 3 remainder 13 |
| 4 | 31 ÷ 13 = 2 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 77 | 2387 |
| 111 and 89 | 9879 |
| 12 and 16 | 48 |
| 28 and 174 | 2436 |
| 139 and 173 | 24047 |