Least Common Multiple (LCM) of 111 and 119
The least common multiple (LCM) of 111 and 119 is 13209.
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 111 and 119?
First, calculate the GCD of 111 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 119 = 0 remainder 111 |
| 2 | 119 ÷ 111 = 1 remainder 8 |
| 3 | 111 ÷ 8 = 13 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 88 | 2728 |
| 162 and 82 | 6642 |
| 138 and 12 | 276 |
| 78 and 49 | 3822 |
| 94 and 69 | 6486 |