Least Common Multiple (LCM) of 111 and 155
The least common multiple (LCM) of 111 and 155 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 111 and 155?
First, calculate the GCD of 111 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 155 = 0 remainder 111 |
| 2 | 155 ÷ 111 = 1 remainder 44 |
| 3 | 111 ÷ 44 = 2 remainder 23 |
| 4 | 44 ÷ 23 = 1 remainder 21 |
| 5 | 23 ÷ 21 = 1 remainder 2 |
| 6 | 21 ÷ 2 = 10 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 52 | 9932 |
| 112 and 130 | 7280 |
| 90 and 106 | 4770 |
| 14 and 176 | 1232 |
| 15 and 125 | 375 |