Least Common Multiple (LCM) of 137 and 37
The least common multiple (LCM) of 137 and 37 is 5069.
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 37?
First, calculate the GCD of 137 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 37 = 3 remainder 26 |
| 2 | 37 ÷ 26 = 1 remainder 11 |
| 3 | 26 ÷ 11 = 2 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 85 | 5695 |
| 68 and 170 | 340 |
| 120 and 137 | 16440 |
| 143 and 27 | 3861 |
| 96 and 15 | 480 |