Least Common Multiple (LCM) of 138 and 59
The least common multiple (LCM) of 138 and 59 is 8142.
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 138 and 59?
First, calculate the GCD of 138 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 59 = 2 remainder 20 |
| 2 | 59 ÷ 20 = 2 remainder 19 |
| 3 | 20 ÷ 19 = 1 remainder 1 |
| 4 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 172 | 3612 |
| 158 and 51 | 8058 |
| 87 and 52 | 4524 |
| 36 and 174 | 1044 |
| 120 and 104 | 1560 |