Least Common Multiple (LCM) of 19 and 108
The least common multiple (LCM) of 19 and 108 is 2052.
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 19 and 108?
First, calculate the GCD of 19 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 108 = 0 remainder 19 |
| 2 | 108 ÷ 19 = 5 remainder 13 |
| 3 | 19 ÷ 13 = 1 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 46 | 1518 |
| 169 and 115 | 19435 |
| 173 and 123 | 21279 |
| 147 and 152 | 22344 |
| 116 and 117 | 13572 |