Least Common Multiple (LCM) of 16 and 24
The least common multiple (LCM) of 16 and 24 is 48.
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 16 and 24?
First, calculate the GCD of 16 and 24 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 24 = 0 remainder 16 |
| 2 | 24 ÷ 16 = 1 remainder 8 |
| 3 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 95 | 11685 |
| 36 and 111 | 1332 |
| 75 and 57 | 1425 |
| 30 and 200 | 600 |
| 146 and 31 | 4526 |