Least Common Multiple (LCM) of 137 and 38
The least common multiple (LCM) of 137 and 38 is 5206.
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 38?
First, calculate the GCD of 137 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 38 = 3 remainder 23 |
| 2 | 38 ÷ 23 = 1 remainder 15 |
| 3 | 23 ÷ 15 = 1 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 37 | 7141 |
| 182 and 112 | 1456 |
| 112 and 95 | 10640 |
| 174 and 120 | 3480 |
| 41 and 18 | 738 |