Least Common Multiple (LCM) of 73 and 169
The least common multiple (LCM) of 73 and 169 is 12337.
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 73 and 169?
First, calculate the GCD of 73 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 169 = 0 remainder 73 |
| 2 | 169 ÷ 73 = 2 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 |
|---|---|
| 73 and 23 | 1679 |
| 140 and 161 | 3220 |
| 50 and 81 | 4050 |
| 107 and 163 | 17441 |
| 55 and 21 | 1155 |