Least Common Multiple (LCM) of 29 and 45
The least common multiple (LCM) of 29 and 45 is 1305.
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 45?
First, calculate the GCD of 29 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 45 = 0 remainder 29 |
| 2 | 45 ÷ 29 = 1 remainder 16 |
| 3 | 29 ÷ 16 = 1 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 65 | 12610 |
| 21 and 142 | 2982 |
| 107 and 102 | 10914 |
| 63 and 45 | 315 |
| 75 and 131 | 9825 |