Least Common Multiple (LCM) of 107 and 166
The least common multiple (LCM) of 107 and 166 is 17762.
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 166?
First, calculate the GCD of 107 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 166 = 0 remainder 107 |
| 2 | 166 ÷ 107 = 1 remainder 59 |
| 3 | 107 ÷ 59 = 1 remainder 48 |
| 4 | 59 ÷ 48 = 1 remainder 11 |
| 5 | 48 ÷ 11 = 4 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 107 | 17869 |
| 75 and 172 | 12900 |
| 83 and 195 | 16185 |
| 101 and 131 | 13231 |
| 195 and 167 | 32565 |