Least Common Multiple (LCM) of 29 and 132
The least common multiple (LCM) of 29 and 132 is 3828.
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 132?
First, calculate the GCD of 29 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 132 = 0 remainder 29 |
| 2 | 132 ÷ 29 = 4 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 |
|---|---|
| 144 and 26 | 1872 |
| 138 and 35 | 4830 |
| 16 and 46 | 368 |
| 184 and 112 | 2576 |
| 129 and 145 | 18705 |