Least Common Multiple (LCM) of 59 and 138
The least common multiple (LCM) of 59 and 138 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 59 and 138?
First, calculate the GCD of 59 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 138 = 0 remainder 59 |
| 2 | 138 ÷ 59 = 2 remainder 20 |
| 3 | 59 ÷ 20 = 2 remainder 19 |
| 4 | 20 ÷ 19 = 1 remainder 1 |
| 5 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 117 | 21879 |
| 38 and 139 | 5282 |
| 20 and 69 | 1380 |
| 141 and 142 | 20022 |
| 113 and 171 | 19323 |