Least Common Multiple (LCM) of 59 and 77
The least common multiple (LCM) of 59 and 77 is 4543.
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 59 and 77?
First, calculate the GCD of 59 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 77 = 0 remainder 59 |
| 2 | 77 ÷ 59 = 1 remainder 18 |
| 3 | 59 ÷ 18 = 3 remainder 5 |
| 4 | 18 ÷ 5 = 3 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 166 | 11786 |
| 149 and 71 | 10579 |
| 56 and 36 | 504 |
| 54 and 71 | 3834 |
| 129 and 136 | 17544 |