Least Common Multiple (LCM) of 59 and 38
The least common multiple (LCM) of 59 and 38 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 59 and 38?
First, calculate the GCD of 59 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 38 = 1 remainder 21 |
| 2 | 38 ÷ 21 = 1 remainder 17 |
| 3 | 21 ÷ 17 = 1 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 38 | 3116 |
| 122 and 197 | 24034 |
| 192 and 126 | 4032 |
| 113 and 187 | 21131 |
| 113 and 80 | 9040 |