Least Common Multiple (LCM) of 138 and 196
The least common multiple (LCM) of 138 and 196 is 13524.
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 196?
First, calculate the GCD of 138 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 196 = 0 remainder 138 |
| 2 | 196 ÷ 138 = 1 remainder 58 |
| 3 | 138 ÷ 58 = 2 remainder 22 |
| 4 | 58 ÷ 22 = 2 remainder 14 |
| 5 | 22 ÷ 14 = 1 remainder 8 |
| 6 | 14 ÷ 8 = 1 remainder 6 |
| 7 | 8 ÷ 6 = 1 remainder 2 |
| 8 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 25 | 2900 |
| 97 and 61 | 5917 |
| 192 and 135 | 8640 |
| 49 and 18 | 882 |
| 116 and 192 | 5568 |