Least Common Multiple (LCM) of 69 and 197
The least common multiple (LCM) of 69 and 197 is 13593.
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 69 and 197?
First, calculate the GCD of 69 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 197 = 0 remainder 69 |
| 2 | 197 ÷ 69 = 2 remainder 59 |
| 3 | 69 ÷ 59 = 1 remainder 10 |
| 4 | 59 ÷ 10 = 5 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 93 | 14136 |
| 119 and 101 | 12019 |
| 175 and 187 | 32725 |
| 55 and 111 | 6105 |
| 113 and 82 | 9266 |