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 |
|---|---|
| 168 and 111 | 6216 |
| 109 and 197 | 21473 |
| 157 and 150 | 23550 |
| 194 and 98 | 9506 |
| 90 and 132 | 1980 |