Least Common Multiple (LCM) of 116 and 102
The least common multiple (LCM) of 116 and 102 is 5916.
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 102?
First, calculate the GCD of 116 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 102 = 1 remainder 14 |
| 2 | 102 ÷ 14 = 7 remainder 4 |
| 3 | 14 ÷ 4 = 3 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 101 | 7575 |
| 81 and 137 | 11097 |
| 178 and 198 | 17622 |
| 40 and 33 | 1320 |
| 19 and 37 | 703 |