Least Common Multiple (LCM) of 77 and 123
The least common multiple (LCM) of 77 and 123 is 9471.
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 123?
First, calculate the GCD of 77 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 123 = 0 remainder 77 |
| 2 | 123 ÷ 77 = 1 remainder 46 |
| 3 | 77 ÷ 46 = 1 remainder 31 |
| 4 | 46 ÷ 31 = 1 remainder 15 |
| 5 | 31 ÷ 15 = 2 remainder 1 |
| 6 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 85 | 2465 |
| 129 and 194 | 25026 |
| 77 and 175 | 1925 |
| 178 and 190 | 16910 |
| 163 and 16 | 2608 |