Least Common Multiple (LCM) of 116 and 138
The least common multiple (LCM) of 116 and 138 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 116 and 138?
First, calculate the GCD of 116 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 138 = 0 remainder 116 |
| 2 | 138 ÷ 116 = 1 remainder 22 |
| 3 | 116 ÷ 22 = 5 remainder 6 |
| 4 | 22 ÷ 6 = 3 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 132 | 528 |
| 124 and 32 | 992 |
| 156 and 188 | 7332 |
| 47 and 122 | 5734 |
| 159 and 181 | 28779 |