Least Common Multiple (LCM) of 77 and 145
The least common multiple (LCM) of 77 and 145 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 77 and 145?
First, calculate the GCD of 77 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 145 = 0 remainder 77 |
| 2 | 145 ÷ 77 = 1 remainder 68 |
| 3 | 77 ÷ 68 = 1 remainder 9 |
| 4 | 68 ÷ 9 = 7 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 172 | 28380 |
| 172 and 86 | 172 |
| 110 and 174 | 9570 |
| 28 and 15 | 420 |
| 200 and 137 | 27400 |