Least Common Multiple (LCM) of 100 and 166
The least common multiple (LCM) of 100 and 166 is 8300.
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 100 and 166?
First, calculate the GCD of 100 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 166 = 0 remainder 100 |
| 2 | 166 ÷ 100 = 1 remainder 66 |
| 3 | 100 ÷ 66 = 1 remainder 34 |
| 4 | 66 ÷ 34 = 1 remainder 32 |
| 5 | 34 ÷ 32 = 1 remainder 2 |
| 6 | 32 ÷ 2 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 44 | 176 |
| 106 and 40 | 2120 |
| 91 and 120 | 10920 |
| 69 and 80 | 5520 |
| 199 and 11 | 2189 |