Least Common Multiple (LCM) of 77 and 104
The least common multiple (LCM) of 77 and 104 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 77 and 104?
First, calculate the GCD of 77 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 104 = 0 remainder 77 |
| 2 | 104 ÷ 77 = 1 remainder 27 |
| 3 | 77 ÷ 27 = 2 remainder 23 |
| 4 | 27 ÷ 23 = 1 remainder 4 |
| 5 | 23 ÷ 4 = 5 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 149 | 3278 |
| 35 and 114 | 3990 |
| 161 and 16 | 2576 |
| 112 and 107 | 11984 |
| 133 and 121 | 16093 |