Least Common Multiple (LCM) of 145 and 111
The least common multiple (LCM) of 145 and 111 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 145 and 111?
First, calculate the GCD of 145 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 111 = 1 remainder 34 |
| 2 | 111 ÷ 34 = 3 remainder 9 |
| 3 | 34 ÷ 9 = 3 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 171 | 3420 |
| 79 and 106 | 8374 |
| 193 and 15 | 2895 |
| 62 and 169 | 10478 |
| 175 and 28 | 700 |