Least Common Multiple (LCM) of 109 and 28
The least common multiple (LCM) of 109 and 28 is 3052.
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 28?
First, calculate the GCD of 109 and 28 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 28 = 3 remainder 25 |
| 2 | 28 ÷ 25 = 1 remainder 3 |
| 3 | 25 ÷ 3 = 8 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 99 | 17622 |
| 59 and 64 | 3776 |
| 26 and 158 | 2054 |
| 89 and 86 | 7654 |
| 181 and 19 | 3439 |