Least Common Multiple (LCM) of 21 and 197
The least common multiple (LCM) of 21 and 197 is 4137.
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 21 and 197?
First, calculate the GCD of 21 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 197 = 0 remainder 21 |
| 2 | 197 ÷ 21 = 9 remainder 8 |
| 3 | 21 ÷ 8 = 2 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 65 | 11115 |
| 166 and 54 | 4482 |
| 116 and 95 | 11020 |
| 115 and 175 | 4025 |
| 90 and 90 | 90 |