Least Common Multiple (LCM) of 109 and 79
The least common multiple (LCM) of 109 and 79 is 8611.
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 79?
First, calculate the GCD of 109 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 79 = 1 remainder 30 |
| 2 | 79 ÷ 30 = 2 remainder 19 |
| 3 | 30 ÷ 19 = 1 remainder 11 |
| 4 | 19 ÷ 11 = 1 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 83 | 6972 |
| 52 and 83 | 4316 |
| 106 and 105 | 11130 |
| 75 and 103 | 7725 |
| 65 and 179 | 11635 |