Least Common Multiple (LCM) of 29 and 113
The least common multiple (LCM) of 29 and 113 is 3277.
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 29 and 113?
First, calculate the GCD of 29 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 113 = 0 remainder 29 |
| 2 | 113 ÷ 29 = 3 remainder 26 |
| 3 | 29 ÷ 26 = 1 remainder 3 |
| 4 | 26 ÷ 3 = 8 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 58 | 11310 |
| 86 and 193 | 16598 |
| 91 and 119 | 1547 |
| 120 and 173 | 20760 |
| 126 and 63 | 126 |