Least Common Multiple (LCM) of 155 and 111
The least common multiple (LCM) of 155 and 111 is 17205.
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 155 and 111?
First, calculate the GCD of 155 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 111 = 1 remainder 44 |
| 2 | 111 ÷ 44 = 2 remainder 23 |
| 3 | 44 ÷ 23 = 1 remainder 21 |
| 4 | 23 ÷ 21 = 1 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 54 | 378 |
| 181 and 178 | 32218 |
| 36 and 108 | 108 |
| 89 and 85 | 7565 |
| 110 and 90 | 990 |