Least Common Multiple (LCM) of 108 and 77
The least common multiple (LCM) of 108 and 77 is 8316.
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 108 and 77?
First, calculate the GCD of 108 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 77 = 1 remainder 31 |
| 2 | 77 ÷ 31 = 2 remainder 15 |
| 3 | 31 ÷ 15 = 2 remainder 1 |
| 4 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 59 | 4307 |
| 115 and 40 | 920 |
| 85 and 56 | 4760 |
| 98 and 171 | 16758 |
| 22 and 165 | 330 |