Least Common Multiple (LCM) of 29 and 73
The least common multiple (LCM) of 29 and 73 is 2117.
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 29 and 73?
First, calculate the GCD of 29 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 73 = 0 remainder 29 |
| 2 | 73 ÷ 29 = 2 remainder 15 |
| 3 | 29 ÷ 15 = 1 remainder 14 |
| 4 | 15 ÷ 14 = 1 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 83 | 13280 |
| 146 and 189 | 27594 |
| 156 and 197 | 30732 |
| 145 and 94 | 13630 |
| 19 and 77 | 1463 |