Least Common Multiple (LCM) of 170 and 111
The least common multiple (LCM) of 170 and 111 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 170 and 111?
First, calculate the GCD of 170 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 111 = 1 remainder 59 |
| 2 | 111 ÷ 59 = 1 remainder 52 |
| 3 | 59 ÷ 52 = 1 remainder 7 |
| 4 | 52 ÷ 7 = 7 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 180 | 5760 |
| 90 and 178 | 8010 |
| 29 and 85 | 2465 |
| 118 and 76 | 4484 |
| 164 and 102 | 8364 |