Least Common Multiple (LCM) of 109 and 77
The least common multiple (LCM) of 109 and 77 is 8393.
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 109 and 77?
First, calculate the GCD of 109 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 77 = 1 remainder 32 |
| 2 | 77 ÷ 32 = 2 remainder 13 |
| 3 | 32 ÷ 13 = 2 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 121 | 605 |
| 33 and 35 | 1155 |
| 32 and 59 | 1888 |
| 104 and 15 | 1560 |
| 62 and 115 | 7130 |