Least Common Multiple (LCM) of 29 and 56
The least common multiple (LCM) of 29 and 56 is 1624.
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 56?
First, calculate the GCD of 29 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 56 = 0 remainder 29 |
| 2 | 56 ÷ 29 = 1 remainder 27 |
| 3 | 29 ÷ 27 = 1 remainder 2 |
| 4 | 27 ÷ 2 = 13 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 26 | 2782 |
| 191 and 120 | 22920 |
| 60 and 10 | 60 |
| 22 and 200 | 2200 |
| 119 and 157 | 18683 |