Least Common Multiple (LCM) of 29 and 135
The least common multiple (LCM) of 29 and 135 is 3915.
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 135?
First, calculate the GCD of 29 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 135 = 0 remainder 29 |
| 2 | 135 ÷ 29 = 4 remainder 19 |
| 3 | 29 ÷ 19 = 1 remainder 10 |
| 4 | 19 ÷ 10 = 1 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 44 | 1892 |
| 101 and 71 | 7171 |
| 154 and 131 | 20174 |
| 188 and 75 | 14100 |
| 21 and 89 | 1869 |