Least Common Multiple (LCM) of 101 and 166
The least common multiple (LCM) of 101 and 166 is 16766.
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 101 and 166?
First, calculate the GCD of 101 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 166 = 0 remainder 101 |
| 2 | 166 ÷ 101 = 1 remainder 65 |
| 3 | 101 ÷ 65 = 1 remainder 36 |
| 4 | 65 ÷ 36 = 1 remainder 29 |
| 5 | 36 ÷ 29 = 1 remainder 7 |
| 6 | 29 ÷ 7 = 4 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 110 | 4290 |
| 103 and 14 | 1442 |
| 186 and 15 | 930 |
| 125 and 15 | 375 |
| 97 and 181 | 17557 |