Least Common Multiple (LCM) of 100 and 181
The least common multiple (LCM) of 100 and 181 is 18100.
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 181?
First, calculate the GCD of 100 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 181 = 0 remainder 100 |
| 2 | 181 ÷ 100 = 1 remainder 81 |
| 3 | 100 ÷ 81 = 1 remainder 19 |
| 4 | 81 ÷ 19 = 4 remainder 5 |
| 5 | 19 ÷ 5 = 3 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 16 | 144 |
| 195 and 112 | 21840 |
| 31 and 159 | 4929 |
| 141 and 191 | 26931 |
| 21 and 120 | 840 |