Least Common Multiple (LCM) of 111 and 170
The least common multiple (LCM) of 111 and 170 is 18870.
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 170?
First, calculate the GCD of 111 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 170 = 0 remainder 111 |
| 2 | 170 ÷ 111 = 1 remainder 59 |
| 3 | 111 ÷ 59 = 1 remainder 52 |
| 4 | 59 ÷ 52 = 1 remainder 7 |
| 5 | 52 ÷ 7 = 7 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 197 | 37824 |
| 134 and 79 | 10586 |
| 65 and 158 | 10270 |
| 48 and 78 | 624 |
| 188 and 121 | 22748 |