Least Common Multiple (LCM) of 105 and 167
The least common multiple (LCM) of 105 and 167 is 17535.
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 105 and 167?
First, calculate the GCD of 105 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 167 = 0 remainder 105 |
| 2 | 167 ÷ 105 = 1 remainder 62 |
| 3 | 105 ÷ 62 = 1 remainder 43 |
| 4 | 62 ÷ 43 = 1 remainder 19 |
| 5 | 43 ÷ 19 = 2 remainder 5 |
| 6 | 19 ÷ 5 = 3 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 63 | 8946 |
| 67 and 43 | 2881 |
| 42 and 125 | 5250 |
| 129 and 173 | 22317 |
| 127 and 60 | 7620 |