Least Common Multiple (LCM) of 111 and 173
The least common multiple (LCM) of 111 and 173 is 19203.
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 173?
First, calculate the GCD of 111 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 173 = 0 remainder 111 |
| 2 | 173 ÷ 111 = 1 remainder 62 |
| 3 | 111 ÷ 62 = 1 remainder 49 |
| 4 | 62 ÷ 49 = 1 remainder 13 |
| 5 | 49 ÷ 13 = 3 remainder 10 |
| 6 | 13 ÷ 10 = 1 remainder 3 |
| 7 | 10 ÷ 3 = 3 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 110 | 990 |
| 98 and 150 | 7350 |
| 103 and 98 | 10094 |
| 105 and 57 | 1995 |
| 89 and 93 | 8277 |