Least Common Multiple (LCM) of 24 and 69
The least common multiple (LCM) of 24 and 69 is 552.
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 24 and 69?
First, calculate the GCD of 24 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 69 = 0 remainder 24 |
| 2 | 69 ÷ 24 = 2 remainder 21 |
| 3 | 24 ÷ 21 = 1 remainder 3 |
| 4 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 110 | 990 |
| 55 and 72 | 3960 |
| 122 and 184 | 11224 |
| 75 and 106 | 7950 |
| 178 and 148 | 13172 |