Least Common Multiple (LCM) of 55 and 148
The least common multiple (LCM) of 55 and 148 is 8140.
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 148?
First, calculate the GCD of 55 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 148 = 0 remainder 55 |
| 2 | 148 ÷ 55 = 2 remainder 38 |
| 3 | 55 ÷ 38 = 1 remainder 17 |
| 4 | 38 ÷ 17 = 2 remainder 4 |
| 5 | 17 ÷ 4 = 4 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 105 | 12810 |
| 41 and 172 | 7052 |
| 177 and 166 | 29382 |
| 29 and 139 | 4031 |
| 25 and 125 | 125 |