Least Common Multiple (LCM) of 170 and 98
The least common multiple (LCM) of 170 and 98 is 8330.
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 170 and 98?
First, calculate the GCD of 170 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 98 = 1 remainder 72 |
| 2 | 98 ÷ 72 = 1 remainder 26 |
| 3 | 72 ÷ 26 = 2 remainder 20 |
| 4 | 26 ÷ 20 = 1 remainder 6 |
| 5 | 20 ÷ 6 = 3 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 111 | 3330 |
| 46 and 149 | 6854 |
| 84 and 107 | 8988 |
| 88 and 144 | 1584 |
| 71 and 138 | 9798 |