Least Common Multiple (LCM) of 98 and 178
The least common multiple (LCM) of 98 and 178 is 8722.
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 178?
First, calculate the GCD of 98 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 178 = 0 remainder 98 |
| 2 | 178 ÷ 98 = 1 remainder 80 |
| 3 | 98 ÷ 80 = 1 remainder 18 |
| 4 | 80 ÷ 18 = 4 remainder 8 |
| 5 | 18 ÷ 8 = 2 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 21 | 777 |
| 116 and 183 | 21228 |
| 20 and 11 | 220 |
| 62 and 141 | 8742 |
| 188 and 81 | 15228 |