Least Common Multiple (LCM) of 29 and 48
The least common multiple (LCM) of 29 and 48 is 1392.
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 48?
First, calculate the GCD of 29 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 48 = 0 remainder 29 |
| 2 | 48 ÷ 29 = 1 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 |
|---|---|
| 192 and 110 | 10560 |
| 118 and 129 | 15222 |
| 154 and 86 | 6622 |
| 107 and 74 | 7918 |
| 189 and 25 | 4725 |