Least Common Multiple (LCM) of 129 and 49
The least common multiple (LCM) of 129 and 49 is 6321.
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 129 and 49?
First, calculate the GCD of 129 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 49 = 2 remainder 31 |
| 2 | 49 ÷ 31 = 1 remainder 18 |
| 3 | 31 ÷ 18 = 1 remainder 13 |
| 4 | 18 ÷ 13 = 1 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 |
|---|---|
| 127 and 50 | 6350 |
| 36 and 131 | 4716 |
| 91 and 184 | 16744 |
| 17 and 100 | 1700 |
| 121 and 188 | 22748 |