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 |
|---|---|
| 164 and 59 | 9676 |
| 31 and 50 | 1550 |
| 116 and 180 | 5220 |
| 21 and 10 | 210 |
| 151 and 109 | 16459 |