Least Common Multiple (LCM) of 111 and 100
The least common multiple (LCM) of 111 and 100 is 11100.
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 111 and 100?
First, calculate the GCD of 111 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 100 = 1 remainder 11 |
| 2 | 100 ÷ 11 = 9 remainder 1 |
| 3 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 53 | 5989 |
| 172 and 82 | 7052 |
| 174 and 195 | 11310 |
| 53 and 105 | 5565 |
| 33 and 131 | 4323 |