Least Common Multiple (LCM) of 17 and 169
The least common multiple (LCM) of 17 and 169 is 2873.
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 17 and 169?
First, calculate the GCD of 17 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 169 = 0 remainder 17 |
| 2 | 169 ÷ 17 = 9 remainder 16 |
| 3 | 17 ÷ 16 = 1 remainder 1 |
| 4 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 178 | 19758 |
| 51 and 154 | 7854 |
| 85 and 169 | 14365 |
| 25 and 19 | 475 |
| 35 and 132 | 4620 |