Least Common Multiple (LCM) of 109 and 24
The least common multiple (LCM) of 109 and 24 is 2616.
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 24?
First, calculate the GCD of 109 and 24 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 24 = 4 remainder 13 |
| 2 | 24 ÷ 13 = 1 remainder 11 |
| 3 | 13 ÷ 11 = 1 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 37 | 7363 |
| 124 and 109 | 13516 |
| 151 and 162 | 24462 |
| 40 and 57 | 2280 |
| 175 and 37 | 6475 |