Least Common Multiple (LCM) of 196 and 138
The least common multiple (LCM) of 196 and 138 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 196 and 138?
First, calculate the GCD of 196 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 138 = 1 remainder 58 |
| 2 | 138 ÷ 58 = 2 remainder 22 |
| 3 | 58 ÷ 22 = 2 remainder 14 |
| 4 | 22 ÷ 14 = 1 remainder 8 |
| 5 | 14 ÷ 8 = 1 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 125 | 18000 |
| 12 and 124 | 372 |
| 20 and 58 | 580 |
| 47 and 136 | 6392 |
| 106 and 96 | 5088 |