Least Common Multiple (LCM) of 106 and 149
The least common multiple (LCM) of 106 and 149 is 15794.
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 149?
First, calculate the GCD of 106 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 149 = 0 remainder 106 |
| 2 | 149 ÷ 106 = 1 remainder 43 |
| 3 | 106 ÷ 43 = 2 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 |
|---|---|
| 75 and 141 | 3525 |
| 164 and 91 | 14924 |
| 171 and 38 | 342 |
| 11 and 59 | 649 |
| 78 and 31 | 2418 |