Least Common Multiple (LCM) of 137 and 56
The least common multiple (LCM) of 137 and 56 is 7672.
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 56?
First, calculate the GCD of 137 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 56 = 2 remainder 25 |
| 2 | 56 ÷ 25 = 2 remainder 6 |
| 3 | 25 ÷ 6 = 4 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 137 | 9727 |
| 156 and 121 | 18876 |
| 39 and 111 | 1443 |
| 41 and 200 | 8200 |
| 46 and 71 | 3266 |