Least Common Multiple (LCM) of 55 and 155
The least common multiple (LCM) of 55 and 155 is 1705.
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 55 and 155?
First, calculate the GCD of 55 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 155 = 0 remainder 55 |
| 2 | 155 ÷ 55 = 2 remainder 45 |
| 3 | 55 ÷ 45 = 1 remainder 10 |
| 4 | 45 ÷ 10 = 4 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 15 | 30 |
| 19 and 137 | 2603 |
| 45 and 80 | 720 |
| 77 and 187 | 1309 |
| 80 and 44 | 880 |