Least Common Multiple (LCM) of 108 and 116
The least common multiple (LCM) of 108 and 116 is 3132.
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 108 and 116?
First, calculate the GCD of 108 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 116 = 0 remainder 108 |
| 2 | 116 ÷ 108 = 1 remainder 8 |
| 3 | 108 ÷ 8 = 13 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 69 | 13317 |
| 129 and 19 | 2451 |
| 165 and 116 | 19140 |
| 152 and 70 | 5320 |
| 103 and 74 | 7622 |