Least Common Multiple (LCM) of 111 and 29
The least common multiple (LCM) of 111 and 29 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 111 and 29?
First, calculate the GCD of 111 and 29 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 29 = 3 remainder 24 |
| 2 | 29 ÷ 24 = 1 remainder 5 |
| 3 | 24 ÷ 5 = 4 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 172 | 13932 |
| 98 and 113 | 11074 |
| 151 and 43 | 6493 |
| 155 and 86 | 13330 |
| 175 and 44 | 7700 |