Least Common Multiple (LCM) of 114 and 146
The least common multiple (LCM) of 114 and 146 is 8322.
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 114 and 146?
First, calculate the GCD of 114 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 146 = 0 remainder 114 |
| 2 | 146 ÷ 114 = 1 remainder 32 |
| 3 | 114 ÷ 32 = 3 remainder 18 |
| 4 | 32 ÷ 18 = 1 remainder 14 |
| 5 | 18 ÷ 14 = 1 remainder 4 |
| 6 | 14 ÷ 4 = 3 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 198 | 13464 |
| 193 and 16 | 3088 |
| 157 and 64 | 10048 |
| 101 and 56 | 5656 |
| 85 and 147 | 12495 |