Least Common Multiple (LCM) of 105 and 38
The least common multiple (LCM) of 105 and 38 is 3990.
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 105 and 38?
First, calculate the GCD of 105 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 38 = 2 remainder 29 |
| 2 | 38 ÷ 29 = 1 remainder 9 |
| 3 | 29 ÷ 9 = 3 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 24 | 600 |
| 160 and 34 | 2720 |
| 137 and 162 | 22194 |
| 22 and 185 | 4070 |
| 42 and 174 | 1218 |