Least Common Multiple (LCM) of 13 and 77
The least common multiple (LCM) of 13 and 77 is 1001.
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 13 and 77?
First, calculate the GCD of 13 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 77 = 0 remainder 13 |
| 2 | 77 ÷ 13 = 5 remainder 12 |
| 3 | 13 ÷ 12 = 1 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 85 | 1020 |
| 196 and 129 | 25284 |
| 81 and 48 | 1296 |
| 188 and 64 | 3008 |
| 116 and 15 | 1740 |