Least Common Multiple (LCM) of 137 and 196
The least common multiple (LCM) of 137 and 196 is 26852.
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 137 and 196?
First, calculate the GCD of 137 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 196 = 0 remainder 137 |
| 2 | 196 ÷ 137 = 1 remainder 59 |
| 3 | 137 ÷ 59 = 2 remainder 19 |
| 4 | 59 ÷ 19 = 3 remainder 2 |
| 5 | 19 ÷ 2 = 9 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 170 | 13430 |
| 179 and 196 | 35084 |
| 75 and 22 | 1650 |
| 158 and 155 | 24490 |
| 70 and 76 | 2660 |