Least Common Multiple (LCM) of 29 and 111
The least common multiple (LCM) of 29 and 111 is 3219.
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 111?
First, calculate the GCD of 29 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 111 = 0 remainder 29 |
| 2 | 111 ÷ 29 = 3 remainder 24 |
| 3 | 29 ÷ 24 = 1 remainder 5 |
| 4 | 24 ÷ 5 = 4 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 44 | 1408 |
| 173 and 11 | 1903 |
| 62 and 165 | 10230 |
| 85 and 86 | 7310 |
| 176 and 169 | 29744 |