Least Common Multiple (LCM) of 35 and 129
The least common multiple (LCM) of 35 and 129 is 4515.
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 35 and 129?
First, calculate the GCD of 35 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 129 = 0 remainder 35 |
| 2 | 129 ÷ 35 = 3 remainder 24 |
| 3 | 35 ÷ 24 = 1 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 166 | 25398 |
| 165 and 79 | 13035 |
| 199 and 175 | 34825 |
| 114 and 158 | 9006 |
| 34 and 168 | 2856 |