Least Common Multiple (LCM) of 19 and 121
The least common multiple (LCM) of 19 and 121 is 2299.
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 121?
First, calculate the GCD of 19 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 121 = 0 remainder 19 |
| 2 | 121 ÷ 19 = 6 remainder 7 |
| 3 | 19 ÷ 7 = 2 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 64 | 2752 |
| 57 and 179 | 10203 |
| 193 and 12 | 2316 |
| 153 and 35 | 5355 |
| 177 and 122 | 21594 |