Least Common Multiple (LCM) of 116 and 25
The least common multiple (LCM) of 116 and 25 is 2900.
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 25?
First, calculate the GCD of 116 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 25 = 4 remainder 16 |
| 2 | 25 ÷ 16 = 1 remainder 9 |
| 3 | 16 ÷ 9 = 1 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 44 | 176 |
| 43 and 141 | 6063 |
| 78 and 55 | 4290 |
| 162 and 98 | 7938 |
| 123 and 62 | 7626 |