Least Common Multiple (LCM) of 98 and 170
The least common multiple (LCM) of 98 and 170 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 98 and 170?
First, calculate the GCD of 98 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 170 = 0 remainder 98 |
| 2 | 170 ÷ 98 = 1 remainder 72 |
| 3 | 98 ÷ 72 = 1 remainder 26 |
| 4 | 72 ÷ 26 = 2 remainder 20 |
| 5 | 26 ÷ 20 = 1 remainder 6 |
| 6 | 20 ÷ 6 = 3 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 35 | 3745 |
| 23 and 190 | 4370 |
| 45 and 172 | 7740 |
| 102 and 112 | 5712 |
| 87 and 38 | 3306 |