Least Common Multiple (LCM) of 16 and 75
The least common multiple (LCM) of 16 and 75 is 1200.
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 75?
First, calculate the GCD of 16 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 75 = 0 remainder 16 |
| 2 | 75 ÷ 16 = 4 remainder 11 |
| 3 | 16 ÷ 11 = 1 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 80 | 8880 |
| 115 and 189 | 21735 |
| 112 and 55 | 6160 |
| 131 and 76 | 9956 |
| 109 and 23 | 2507 |