Least Common Multiple (LCM) of 116 and 146
The least common multiple (LCM) of 116 and 146 is 8468.
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 146?
First, calculate the GCD of 116 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 146 = 0 remainder 116 |
| 2 | 146 ÷ 116 = 1 remainder 30 |
| 3 | 116 ÷ 30 = 3 remainder 26 |
| 4 | 30 ÷ 26 = 1 remainder 4 |
| 5 | 26 ÷ 4 = 6 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 45 | 1305 |
| 80 and 79 | 6320 |
| 176 and 31 | 5456 |
| 42 and 120 | 840 |
| 102 and 196 | 9996 |