Least Common Multiple (LCM) of 169 and 19
The least common multiple (LCM) of 169 and 19 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 169 and 19?
First, calculate the GCD of 169 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 19 = 8 remainder 17 |
| 2 | 19 ÷ 17 = 1 remainder 2 |
| 3 | 17 ÷ 2 = 8 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 106 | 17490 |
| 104 and 175 | 18200 |
| 112 and 19 | 2128 |
| 21 and 47 | 987 |
| 174 and 91 | 15834 |