Least Common Multiple (LCM) of 110 and 155
The least common multiple (LCM) of 110 and 155 is 3410.
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 110 and 155?
First, calculate the GCD of 110 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 155 = 0 remainder 110 |
| 2 | 155 ÷ 110 = 1 remainder 45 |
| 3 | 110 ÷ 45 = 2 remainder 20 |
| 4 | 45 ÷ 20 = 2 remainder 5 |
| 5 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 156 | 1716 |
| 134 and 76 | 5092 |
| 80 and 188 | 3760 |
| 111 and 81 | 2997 |
| 165 and 106 | 17490 |