Least Common Multiple (LCM) of 29 and 54
The least common multiple (LCM) of 29 and 54 is 1566.
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 54?
First, calculate the GCD of 29 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 54 = 0 remainder 29 |
| 2 | 54 ÷ 29 = 1 remainder 25 |
| 3 | 29 ÷ 25 = 1 remainder 4 |
| 4 | 25 ÷ 4 = 6 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 179 | 8234 |
| 143 and 84 | 12012 |
| 148 and 34 | 2516 |
| 104 and 88 | 1144 |
| 114 and 175 | 19950 |