Least Common Multiple (LCM) of 197 and 55
The least common multiple (LCM) of 197 and 55 is 10835.
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 197 and 55?
First, calculate the GCD of 197 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 55 = 3 remainder 32 |
| 2 | 55 ÷ 32 = 1 remainder 23 |
| 3 | 32 ÷ 23 = 1 remainder 9 |
| 4 | 23 ÷ 9 = 2 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 163 | 6683 |
| 90 and 113 | 10170 |
| 168 and 136 | 2856 |
| 18 and 31 | 558 |
| 81 and 36 | 324 |