Least Common Multiple (LCM) of 16 and 45
The least common multiple (LCM) of 16 and 45 is 720.
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 45?
First, calculate the GCD of 16 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 45 = 0 remainder 16 |
| 2 | 45 ÷ 16 = 2 remainder 13 |
| 3 | 16 ÷ 13 = 1 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 48 | 9168 |
| 196 and 47 | 9212 |
| 154 and 150 | 11550 |
| 140 and 32 | 1120 |
| 124 and 197 | 24428 |