Least Common Multiple (LCM) of 155 and 192
The least common multiple (LCM) of 155 and 192 is 29760.
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 192?
First, calculate the GCD of 155 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 192 = 0 remainder 155 |
| 2 | 192 ÷ 155 = 1 remainder 37 |
| 3 | 155 ÷ 37 = 4 remainder 7 |
| 4 | 37 ÷ 7 = 5 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 21 | 1260 |
| 159 and 57 | 3021 |
| 30 and 32 | 480 |
| 37 and 104 | 3848 |
| 175 and 128 | 22400 |