Least Common Multiple (LCM) of 87 and 198
The least common multiple (LCM) of 87 and 198 is 5742.
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 198?
First, calculate the GCD of 87 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 198 = 0 remainder 87 |
| 2 | 198 ÷ 87 = 2 remainder 24 |
| 3 | 87 ÷ 24 = 3 remainder 15 |
| 4 | 24 ÷ 15 = 1 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 65 | 12740 |
| 30 and 192 | 960 |
| 92 and 145 | 13340 |
| 143 and 56 | 8008 |
| 78 and 180 | 2340 |