Least Common Multiple (LCM) of 111 and 145
The least common multiple (LCM) of 111 and 145 is 16095.
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 145?
First, calculate the GCD of 111 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 145 = 0 remainder 111 |
| 2 | 145 ÷ 111 = 1 remainder 34 |
| 3 | 111 ÷ 34 = 3 remainder 9 |
| 4 | 34 ÷ 9 = 3 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 191 | 19100 |
| 55 and 34 | 1870 |
| 69 and 30 | 690 |
| 42 and 39 | 546 |
| 32 and 191 | 6112 |