Least Common Multiple (LCM) of 38 and 104
The least common multiple (LCM) of 38 and 104 is 1976.
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 104?
First, calculate the GCD of 38 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 104 = 0 remainder 38 |
| 2 | 104 ÷ 38 = 2 remainder 28 |
| 3 | 38 ÷ 28 = 1 remainder 10 |
| 4 | 28 ÷ 10 = 2 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 31 | 5580 |
| 36 and 59 | 2124 |
| 188 and 114 | 10716 |
| 44 and 103 | 4532 |
| 33 and 188 | 6204 |