Least Common Multiple (LCM) of 138 and 98
The least common multiple (LCM) of 138 and 98 is 6762.
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 138 and 98?
First, calculate the GCD of 138 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 98 = 1 remainder 40 |
| 2 | 98 ÷ 40 = 2 remainder 18 |
| 3 | 40 ÷ 18 = 2 remainder 4 |
| 4 | 18 ÷ 4 = 4 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 85 | 11305 |
| 130 and 84 | 5460 |
| 172 and 32 | 1376 |
| 40 and 187 | 7480 |
| 26 and 78 | 78 |