Least Common Multiple (LCM) of 170 and 67
The least common multiple (LCM) of 170 and 67 is 11390.
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 67?
First, calculate the GCD of 170 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 67 = 2 remainder 36 |
| 2 | 67 ÷ 36 = 1 remainder 31 |
| 3 | 36 ÷ 31 = 1 remainder 5 |
| 4 | 31 ÷ 5 = 6 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 37 | 2220 |
| 197 and 113 | 22261 |
| 12 and 68 | 204 |
| 109 and 100 | 10900 |
| 114 and 107 | 12198 |