Least Common Multiple (LCM) of 100 and 111
The least common multiple (LCM) of 100 and 111 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 100 and 111?
First, calculate the GCD of 100 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 111 = 0 remainder 100 |
| 2 | 111 ÷ 100 = 1 remainder 11 |
| 3 | 100 ÷ 11 = 9 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 54 | 9126 |
| 21 and 170 | 3570 |
| 19 and 161 | 3059 |
| 11 and 55 | 55 |
| 76 and 196 | 3724 |