Least Common Multiple (LCM) of 169 and 191
The least common multiple (LCM) of 169 and 191 is 32279.
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 191?
First, calculate the GCD of 169 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 191 = 0 remainder 169 |
| 2 | 191 ÷ 169 = 1 remainder 22 |
| 3 | 169 ÷ 22 = 7 remainder 15 |
| 4 | 22 ÷ 15 = 1 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 192 | 960 |
| 193 and 44 | 8492 |
| 106 and 29 | 3074 |
| 160 and 120 | 480 |
| 37 and 172 | 6364 |