Least Common Multiple (LCM) of 38 and 137
The least common multiple (LCM) of 38 and 137 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 38 and 137?
First, calculate the GCD of 38 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 137 = 0 remainder 38 |
| 2 | 137 ÷ 38 = 3 remainder 23 |
| 3 | 38 ÷ 23 = 1 remainder 15 |
| 4 | 23 ÷ 15 = 1 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 188 | 15228 |
| 75 and 115 | 1725 |
| 89 and 117 | 10413 |
| 120 and 97 | 11640 |
| 72 and 166 | 5976 |