Least Common Multiple (LCM) of 87 and 197
The least common multiple (LCM) of 87 and 197 is 17139.
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 87 and 197?
First, calculate the GCD of 87 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 197 = 0 remainder 87 |
| 2 | 197 ÷ 87 = 2 remainder 23 |
| 3 | 87 ÷ 23 = 3 remainder 18 |
| 4 | 23 ÷ 18 = 1 remainder 5 |
| 5 | 18 ÷ 5 = 3 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 21 | 525 |
| 68 and 127 | 8636 |
| 154 and 76 | 5852 |
| 96 and 190 | 9120 |
| 120 and 170 | 2040 |