Least Common Multiple (LCM) of 107 and 167
The least common multiple (LCM) of 107 and 167 is 17869.
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 107 and 167?
First, calculate the GCD of 107 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 167 = 0 remainder 107 |
| 2 | 167 ÷ 107 = 1 remainder 60 |
| 3 | 107 ÷ 60 = 1 remainder 47 |
| 4 | 60 ÷ 47 = 1 remainder 13 |
| 5 | 47 ÷ 13 = 3 remainder 8 |
| 6 | 13 ÷ 8 = 1 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 192 | 29760 |
| 72 and 131 | 9432 |
| 12 and 70 | 420 |
| 100 and 78 | 3900 |
| 15 and 23 | 345 |