Least Common Multiple (LCM) of 103 and 77
The least common multiple (LCM) of 103 and 77 is 7931.
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 103 and 77?
First, calculate the GCD of 103 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 77 = 1 remainder 26 |
| 2 | 77 ÷ 26 = 2 remainder 25 |
| 3 | 26 ÷ 25 = 1 remainder 1 |
| 4 | 25 ÷ 1 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 136 | 2040 |
| 60 and 92 | 1380 |
| 162 and 124 | 10044 |
| 140 and 92 | 3220 |
| 138 and 122 | 8418 |