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 |
|---|---|
| 55 and 18 | 990 |
| 110 and 133 | 14630 |
| 68 and 50 | 1700 |
| 194 and 61 | 11834 |
| 199 and 119 | 23681 |