Least Common Multiple (LCM) of 13 and 24
The least common multiple (LCM) of 13 and 24 is 312.
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 13 and 24?
First, calculate the GCD of 13 and 24 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 24 = 0 remainder 13 |
| 2 | 24 ÷ 13 = 1 remainder 11 |
| 3 | 13 ÷ 11 = 1 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 157 | 23236 |
| 79 and 61 | 4819 |
| 114 and 175 | 19950 |
| 188 and 154 | 14476 |
| 138 and 33 | 1518 |