Least Common Multiple (LCM) of 78 and 146
The least common multiple (LCM) of 78 and 146 is 5694.
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 78 and 146?
First, calculate the GCD of 78 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 146 = 0 remainder 78 |
| 2 | 146 ÷ 78 = 1 remainder 68 |
| 3 | 78 ÷ 68 = 1 remainder 10 |
| 4 | 68 ÷ 10 = 6 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 75 | 525 |
| 25 and 176 | 4400 |
| 21 and 67 | 1407 |
| 30 and 117 | 1170 |
| 158 and 24 | 1896 |