Least Common Multiple (LCM) of 169 and 106
The least common multiple (LCM) of 169 and 106 is 17914.
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 106?
First, calculate the GCD of 169 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 106 = 1 remainder 63 |
| 2 | 106 ÷ 63 = 1 remainder 43 |
| 3 | 63 ÷ 43 = 1 remainder 20 |
| 4 | 43 ÷ 20 = 2 remainder 3 |
| 5 | 20 ÷ 3 = 6 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 64 | 4544 |
| 96 and 88 | 1056 |
| 109 and 99 | 10791 |
| 14 and 136 | 952 |
| 185 and 16 | 2960 |