Least Common Multiple (LCM) of 166 and 107
The least common multiple (LCM) of 166 and 107 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 166 and 107?
First, calculate the GCD of 166 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 166 ÷ 107 = 1 remainder 59 |
| 2 | 107 ÷ 59 = 1 remainder 48 |
| 3 | 59 ÷ 48 = 1 remainder 11 |
| 4 | 48 ÷ 11 = 4 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 114 | 114 |
| 143 and 90 | 12870 |
| 172 and 83 | 14276 |
| 31 and 28 | 868 |
| 179 and 183 | 32757 |