Least Common Multiple (LCM) of 109 and 76
The least common multiple (LCM) of 109 and 76 is 8284.
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 76?
First, calculate the GCD of 109 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 76 = 1 remainder 33 |
| 2 | 76 ÷ 33 = 2 remainder 10 |
| 3 | 33 ÷ 10 = 3 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 48 | 48 |
| 40 and 14 | 280 |
| 145 and 91 | 13195 |
| 128 and 14 | 896 |
| 72 and 78 | 936 |