Least Common Multiple (LCM) of 29 and 52
The least common multiple (LCM) of 29 and 52 is 1508.
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 52?
First, calculate the GCD of 29 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 52 = 0 remainder 29 |
| 2 | 52 ÷ 29 = 1 remainder 23 |
| 3 | 29 ÷ 23 = 1 remainder 6 |
| 4 | 23 ÷ 6 = 3 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 125 | 4125 |
| 85 and 63 | 5355 |
| 102 and 114 | 1938 |
| 10 and 128 | 640 |
| 169 and 78 | 1014 |