Least Common Multiple (LCM) of 78 and 145
The least common multiple (LCM) of 78 and 145 is 11310.
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 145?
First, calculate the GCD of 78 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 145 = 0 remainder 78 |
| 2 | 145 ÷ 78 = 1 remainder 67 |
| 3 | 78 ÷ 67 = 1 remainder 11 |
| 4 | 67 ÷ 11 = 6 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 46 | 506 |
| 68 and 21 | 1428 |
| 74 and 169 | 12506 |
| 77 and 194 | 14938 |
| 20 and 32 | 160 |