Least Common Multiple (LCM) of 98 and 171
The least common multiple (LCM) of 98 and 171 is 16758.
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 98 and 171?
First, calculate the GCD of 98 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 171 = 0 remainder 98 |
| 2 | 171 ÷ 98 = 1 remainder 73 |
| 3 | 98 ÷ 73 = 1 remainder 25 |
| 4 | 73 ÷ 25 = 2 remainder 23 |
| 5 | 25 ÷ 23 = 1 remainder 2 |
| 6 | 23 ÷ 2 = 11 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 54 | 7506 |
| 20 and 175 | 700 |
| 166 and 197 | 32702 |
| 72 and 21 | 504 |
| 193 and 101 | 19493 |