Least Common Multiple (LCM) of 169 and 49
The least common multiple (LCM) of 169 and 49 is 8281.
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 49?
First, calculate the GCD of 169 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 49 = 3 remainder 22 |
| 2 | 49 ÷ 22 = 2 remainder 5 |
| 3 | 22 ÷ 5 = 4 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 193 | 20072 |
| 38 and 165 | 6270 |
| 141 and 186 | 8742 |
| 185 and 110 | 4070 |
| 84 and 80 | 1680 |