Least Common Multiple (LCM) of 24 and 110
The least common multiple (LCM) of 24 and 110 is 1320.
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 110?
First, calculate the GCD of 24 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 110 = 0 remainder 24 |
| 2 | 110 ÷ 24 = 4 remainder 14 |
| 3 | 24 ÷ 14 = 1 remainder 10 |
| 4 | 14 ÷ 10 = 1 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 113 | 10848 |
| 187 and 115 | 21505 |
| 57 and 119 | 6783 |
| 108 and 103 | 11124 |
| 13 and 47 | 611 |