Least Common Multiple (LCM) of 111 and 118
The least common multiple (LCM) of 111 and 118 is 13098.
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 118?
First, calculate the GCD of 111 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 118 = 0 remainder 111 |
| 2 | 118 ÷ 111 = 1 remainder 7 |
| 3 | 111 ÷ 7 = 15 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 71 | 10934 |
| 40 and 45 | 360 |
| 22 and 111 | 2442 |
| 61 and 198 | 12078 |
| 123 and 13 | 1599 |