Least Common Multiple (LCM) of 38 and 59
The least common multiple (LCM) of 38 and 59 is 2242.
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 59?
First, calculate the GCD of 38 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 59 = 0 remainder 38 |
| 2 | 59 ÷ 38 = 1 remainder 21 |
| 3 | 38 ÷ 21 = 1 remainder 17 |
| 4 | 21 ÷ 17 = 1 remainder 4 |
| 5 | 17 ÷ 4 = 4 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 164 | 31324 |
| 200 and 17 | 3400 |
| 132 and 89 | 11748 |
| 55 and 83 | 4565 |
| 34 and 106 | 1802 |