Least Common Multiple (LCM) of 38 and 145
The least common multiple (LCM) of 38 and 145 is 5510.
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 145?
First, calculate the GCD of 38 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 145 = 0 remainder 38 |
| 2 | 145 ÷ 38 = 3 remainder 31 |
| 3 | 38 ÷ 31 = 1 remainder 7 |
| 4 | 31 ÷ 7 = 4 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 127 | 13716 |
| 46 and 75 | 3450 |
| 198 and 103 | 20394 |
| 13 and 162 | 2106 |
| 175 and 97 | 16975 |