Least Common Multiple (LCM) of 104 and 77
The least common multiple (LCM) of 104 and 77 is 8008.
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 104 and 77?
First, calculate the GCD of 104 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 77 = 1 remainder 27 |
| 2 | 77 ÷ 27 = 2 remainder 23 |
| 3 | 27 ÷ 23 = 1 remainder 4 |
| 4 | 23 ÷ 4 = 5 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 49 | 8428 |
| 140 and 155 | 4340 |
| 37 and 148 | 148 |
| 169 and 81 | 13689 |
| 46 and 166 | 3818 |