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 |
|---|---|
| 178 and 114 | 10146 |
| 95 and 193 | 18335 |
| 94 and 176 | 8272 |
| 35 and 195 | 1365 |
| 85 and 123 | 10455 |