Least Common Multiple (LCM) of 129 and 53
The least common multiple (LCM) of 129 and 53 is 6837.
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 53?
First, calculate the GCD of 129 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 53 = 2 remainder 23 |
| 2 | 53 ÷ 23 = 2 remainder 7 |
| 3 | 23 ÷ 7 = 3 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 24 | 264 |
| 178 and 114 | 10146 |
| 136 and 69 | 9384 |
| 109 and 93 | 10137 |
| 89 and 66 | 5874 |