Least Common Multiple (LCM) of 138 and 116
The least common multiple (LCM) of 138 and 116 is 8004.
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 116?
First, calculate the GCD of 138 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 116 = 1 remainder 22 |
| 2 | 116 ÷ 22 = 5 remainder 6 |
| 3 | 22 ÷ 6 = 3 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 24 | 3336 |
| 174 and 200 | 17400 |
| 60 and 181 | 10860 |
| 166 and 156 | 12948 |
| 102 and 101 | 10302 |