Least Common Multiple (LCM) of 105 and 24
The least common multiple (LCM) of 105 and 24 is 840.
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 105 and 24?
First, calculate the GCD of 105 and 24 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 24 = 4 remainder 9 |
| 2 | 24 ÷ 9 = 2 remainder 6 |
| 3 | 9 ÷ 6 = 1 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 63 | 4095 |
| 11 and 200 | 2200 |
| 38 and 135 | 5130 |
| 126 and 97 | 12222 |
| 83 and 60 | 4980 |