Least Common Multiple (LCM) of 19 and 169
The least common multiple (LCM) of 19 and 169 is 3211.
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 169?
First, calculate the GCD of 19 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 169 = 0 remainder 19 |
| 2 | 169 ÷ 19 = 8 remainder 17 |
| 3 | 19 ÷ 17 = 1 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 196 | 15876 |
| 128 and 127 | 16256 |
| 109 and 53 | 5777 |
| 156 and 54 | 1404 |
| 152 and 110 | 8360 |