Least Common Multiple (LCM) of 99 and 118
The least common multiple (LCM) of 99 and 118 is 11682.
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 99 and 118?
First, calculate the GCD of 99 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 118 = 0 remainder 99 |
| 2 | 118 ÷ 99 = 1 remainder 19 |
| 3 | 99 ÷ 19 = 5 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 150 | 8400 |
| 51 and 183 | 3111 |
| 75 and 200 | 600 |
| 16 and 48 | 48 |
| 39 and 17 | 663 |