Least Common Multiple (LCM) of 145 and 77
The least common multiple (LCM) of 145 and 77 is 11165.
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 145 and 77?
First, calculate the GCD of 145 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 77 = 1 remainder 68 |
| 2 | 77 ÷ 68 = 1 remainder 9 |
| 3 | 68 ÷ 9 = 7 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 137 | 5617 |
| 186 and 112 | 10416 |
| 11 and 165 | 165 |
| 40 and 192 | 960 |
| 29 and 158 | 4582 |