Least Common Multiple (LCM) of 16 and 123
The least common multiple (LCM) of 16 and 123 is 1968.
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 123?
First, calculate the GCD of 16 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 123 = 0 remainder 16 |
| 2 | 123 ÷ 16 = 7 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 |
|---|---|
| 129 and 108 | 4644 |
| 39 and 186 | 2418 |
| 149 and 141 | 21009 |
| 15 and 158 | 2370 |
| 81 and 29 | 2349 |