Least Common Multiple (LCM) of 55 and 196
The least common multiple (LCM) of 55 and 196 is 10780.
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 196?
First, calculate the GCD of 55 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 196 = 0 remainder 55 |
| 2 | 196 ÷ 55 = 3 remainder 31 |
| 3 | 55 ÷ 31 = 1 remainder 24 |
| 4 | 31 ÷ 24 = 1 remainder 7 |
| 5 | 24 ÷ 7 = 3 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 77 | 308 |
| 69 and 167 | 11523 |
| 35 and 77 | 385 |
| 57 and 67 | 3819 |
| 180 and 187 | 33660 |