Least Common Multiple (LCM) of 24 and 159
The least common multiple (LCM) of 24 and 159 is 1272.
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 159?
First, calculate the GCD of 24 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 159 = 0 remainder 24 |
| 2 | 159 ÷ 24 = 6 remainder 15 |
| 3 | 24 ÷ 15 = 1 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 103 | 11639 |
| 100 and 132 | 3300 |
| 75 and 32 | 2400 |
| 161 and 11 | 1771 |
| 29 and 190 | 5510 |