Least Common Multiple (LCM) of 99 and 119
The least common multiple (LCM) of 99 and 119 is 11781.
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 119?
First, calculate the GCD of 99 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 119 = 0 remainder 99 |
| 2 | 119 ÷ 99 = 1 remainder 20 |
| 3 | 99 ÷ 20 = 4 remainder 19 |
| 4 | 20 ÷ 19 = 1 remainder 1 |
| 5 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 66 | 1518 |
| 161 and 99 | 15939 |
| 91 and 141 | 12831 |
| 162 and 44 | 3564 |
| 55 and 63 | 3465 |