Least Common Multiple (LCM) of 66 and 169
The least common multiple (LCM) of 66 and 169 is 11154.
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 66 and 169?
First, calculate the GCD of 66 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 169 = 0 remainder 66 |
| 2 | 169 ÷ 66 = 2 remainder 37 |
| 3 | 66 ÷ 37 = 1 remainder 29 |
| 4 | 37 ÷ 29 = 1 remainder 8 |
| 5 | 29 ÷ 8 = 3 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 42 | 1680 |
| 99 and 195 | 6435 |
| 122 and 101 | 12322 |
| 20 and 142 | 1420 |
| 195 and 78 | 390 |