Least Common Multiple (LCM) of 17 and 167
The least common multiple (LCM) of 17 and 167 is 2839.
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 17 and 167?
First, calculate the GCD of 17 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 167 = 0 remainder 17 |
| 2 | 167 ÷ 17 = 9 remainder 14 |
| 3 | 17 ÷ 14 = 1 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 91 | 1729 |
| 153 and 198 | 3366 |
| 11 and 54 | 594 |
| 129 and 89 | 11481 |
| 173 and 33 | 5709 |