Least Common Multiple (LCM) of 169 and 96
The least common multiple (LCM) of 169 and 96 is 16224.
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 96?
First, calculate the GCD of 169 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 96 = 1 remainder 73 |
| 2 | 96 ÷ 73 = 1 remainder 23 |
| 3 | 73 ÷ 23 = 3 remainder 4 |
| 4 | 23 ÷ 4 = 5 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 133 | 13832 |
| 172 and 193 | 33196 |
| 24 and 126 | 504 |
| 17 and 60 | 1020 |
| 173 and 52 | 8996 |