Least Common Multiple (LCM) of 55 and 30
The least common multiple (LCM) of 55 and 30 is 330.
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 30?
First, calculate the GCD of 55 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 30 = 1 remainder 25 |
| 2 | 30 ÷ 25 = 1 remainder 5 |
| 3 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 127 | 17145 |
| 133 and 128 | 17024 |
| 198 and 132 | 396 |
| 170 and 200 | 3400 |
| 40 and 192 | 960 |