Least Common Multiple (LCM) of 106 and 79
The least common multiple (LCM) of 106 and 79 is 8374.
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 106 and 79?
First, calculate the GCD of 106 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 79 = 1 remainder 27 |
| 2 | 79 ÷ 27 = 2 remainder 25 |
| 3 | 27 ÷ 25 = 1 remainder 2 |
| 4 | 25 ÷ 2 = 12 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 164 | 4592 |
| 71 and 184 | 13064 |
| 53 and 134 | 7102 |
| 16 and 170 | 1360 |
| 18 and 176 | 1584 |