Least Common Multiple (LCM) of 29 and 65
The least common multiple (LCM) of 29 and 65 is 1885.
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 65?
First, calculate the GCD of 29 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 65 = 0 remainder 29 |
| 2 | 65 ÷ 29 = 2 remainder 7 |
| 3 | 29 ÷ 7 = 4 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 120 | 3480 |
| 156 and 181 | 28236 |
| 44 and 99 | 396 |
| 140 and 75 | 2100 |
| 107 and 109 | 11663 |