Least Common Multiple (LCM) of 49 and 169
The least common multiple (LCM) of 49 and 169 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 49 and 169?
First, calculate the GCD of 49 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 169 = 0 remainder 49 |
| 2 | 169 ÷ 49 = 3 remainder 22 |
| 3 | 49 ÷ 22 = 2 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 34 | 4726 |
| 165 and 136 | 22440 |
| 76 and 165 | 12540 |
| 141 and 112 | 15792 |
| 17 and 181 | 3077 |